measuring sap flow and stem water content in trees: a critical ...measuring sap flow and stem water...
TRANSCRIPT
Measuring sap flow and stem water
content in trees: a critical analysis and
development of a new heat pulse
method (Sapflow+)
1
2
3
Thesis
submitted in fulfillment of the requirements for the degree of
Doctor (PhD) in Applied Biological Sciences
by
ir. Maurits Vandegehuchte
May 2013
Promoter
Prof. dr. ir. Kathy STEPPE
Department of Applied Biology and Environmental Biology,
Laboratory of Plant Ecology, Universiteit Gent
Members of the examination board
Prof. dr. ir. Patrick VAN DAMME
Department of Plant Production,
Laboratory of Tropical and Subtropical Agriculture and Ethnobotany,
Universiteit Gent
Prof. dr. ir. Wim CORNELIS
Department of Soil Management,
Soil Physics SOPHY, Universiteit Gent
Prof. dr. Nico KOEDAM
Department of Biology,
Laboratory of Plant Biology and Nature Management, Vrije Universiteit
Brussel
Prof. dr. ir. Kris VERHEYEN
Department of Forest and Water Management,
Forest and Nature Lab, Universiteit Gent
Prof. dr. Caroline VINCKE
Earth and Life Institute,
Forest Science and Engineering, Université Catholique de Louvain
Dr. Melanie ZEPPEL
Department of Biological Sciences,
Climate and Forest Ecosystem Modelling group, Macquarie University
Dean
Prof. dr. ir. Guido VAN HUYLENBROECK
Rector
Prof. dr. Paul VAN CAUWENBERGE
The research reported in this thesis was conducted at the Department of Applied
Ecology and Environmental Biology (Laboratory of Plant Ecology) of the Ghent
University, Belgium. This research and the research stay on North Stradbroke Island
were funded by the Research Foundation – Flanders (FWO, Flanders, Belgium). The
author is a PhD fellow of the FWO-Flanders.
Dutch translation of the title:
Meten van sapstroom en stamwaterinhoud in bomen: een kritische analyse en
ontwikkeling van een nieuwe warmtepuls methode (Sapflow+)
Citation of this thesis:
Vandegehuchte, M. W. (2013). Measuring sap flow and stem water content in trees: a
critical analysis and development of a new heat pulse method (Sapflow+). PhD
thesis, Ghent University, Belgium.
ISBN-number: 978-90-5989-610-9
The author and the promoter give the authorisation to consult and to copy parts of
this work for personal use only. Every other use is subject to the copyright laws.
Permission to reproduce any material contained in this work should be obtained
from the author.
i
Acknowledgement - Dankwoord
Beste lezer, u behoort ongetwijfeld tot één van twee grote lezersgroepen. De ene
groep bestaat uit zij die dit werk volledig doorlezen of hier en daar de delen eruit
pikken waarin ze, vanuit wetenschappelijk oogpunt, geïnteresseerd zijn. De tweede
zijn zij die enkel deze eerste bladzijden lezen uit interesse voor het meer
menselijke aspect van de wetenschap of wie weet, in de hoop er ergens hun naam in
terug te vinden. Toch zijn beide groepen voor dit doctoraat even belangrijk geweest.
Ik hoop dan ook dat deze eerste en alle daaropvolgende bladzijden niemand van
deze beide groepen teleur zullen stellen.
Ten eerste wil ik mijn promotor, Kathy Steppe, bedanken. Niet omdat het zo hoort,
wel omdat er niemand anders is die zoveel tot dit werk heeft bijgedragen als jij. Vier
jaar geleden zorgde je enthousiasme als lesgever ervoor dat ik mijn thesis bij het
Labo Plantecologie wou doen. Na een avontuur in Tunesië spoorde je me aan om te
beginnen doctoreren en hielp je me mijn FWO beurs binnen te halen. Sindsdien heb
ik altijd met veel plezier met je samen gewerkt. Je hielp me ideeën uitdenken en
uitdagingen aan te gaan, waarbij je enthousiasme aanstekelijk werkte. Daarnaast
verloor je nooit je geduld als ik weer eens een veel te gehaaste versie van een paper
doorstuurde en jij er nauwgezet alle schrijf- en schoonheidsfoutjes uithaalde.
Bovendien steunde je me steeds in mijn wilde plannen om een bestaande theorie op
de korrel te nemen, in bomen te gaan slingeren of de gevaren van de mangroves te
trotseren. En naast het wetenschappelijke aspect was er steeds tijd voor een leuke
babbel of een toffe activiteit, of het nu in schaatsen in de buurt van Gent was of een
kampvuur in de bergen van Obora. Bedankt om voor mij zoveel deuren te openen,
mij te blijven vertrouwen in mijn werk en voor je creatieve inbreng in wat we tot
Acknowledgement
ii
stand hebben gebracht. Ik hoop dan ook dat ik nog een tijdje deel kan uitmaken van
de toffe bende die het Labo Plantecologie onder jouw leiding geworden is.
Dat brengt ons naadloos bij de rest van de bende, zonder wie het labo maar een
stille en lege plaats zou zijn. Bedankt aan iedereen voor de gezellige koffiepauzes,
middagpauzes, uitgelopen labo activiteiten en zoveel meer. De doc’s (Tommeke,
Hans, Veerle en Wouter) wil ik bedanken om mij drie jaar geleden als groentje op te
nemen in de groep. Nachtelijke zwempartijen, in bomen klimmen en avondlijke
pintjes waren een goede afwisseling tussen het wetenschappelijke werk door, ik
hoop dan ook dat er nog veel dergelijke ondernemingen mogen volgen! Tom,
hopelijk zien we je af en toe nog eens opduiken nu je bij ILVO werkt. Wouter, veel
succes in Australië, als je iemand nodig hebt om de mangroves in te duiken, weet je
me te vinden. Hans, hopelijk kan ik je binnenkort prof noemen en mag ik eens wat
sapstroom gaan meten op je lianen. Veerle, nogmaals sorry voor het stelen van uw
bureau. Jasper en Annelies, van studiegenoten zijn we geëvolueerd tot collega’s.
Bedankt voor die leuke eerste jaren op ons eiland. En dan is er natuurlijk ook de
‘nieuwere’ generatie. Naast Jochen en Marjolein, wil ik vooral Lidewei, Elizabeth,
Ingvar en Bart bedanken voor de fijne momenten op ‘onze’ bureau. Muren
intrappen, pseudowetenschappelijke discussies voeren en al typend met twee
vingers ‘hard werken’ heeft al voor veel plezante momenten gezorgd.
En dan kom ik bij de eigenlijke helden van ons labo: Geert en Philip. Zonder jullie
was dit boekje er niet geweest. De vele uren die jullie hebben besteed aan het mee
ontwerpen en maken van sensoren, het omhakken van bomen (met gevaar voor
eigen leven), het installeren van de gemaakte sensoren, heen en weer rijden naar
Wageningen en Gontrode… ze zijn ontelbaar. Om nog maar te zwijgen van de
laatste spurt voor ik naar Australië vertrok. Het samenwerken was altijd een
genoegen, de frietjes tussendoor meer dan verdiend. En nu dit boekje er ligt, wordt
het tijd om de belofte in te lossen: ‘het stoveke’ wacht op jullie… Natuurlijk wil ik
hier ook de latere aanvulling van het technisch team bedanken. Erik en Thomas,
zonder jullie was de Sapflow+ er niet geweest in zijn huidige vorm. Ann, Margot en
Pui Yi, jullie counterden mijn slordigheid met administratieve punctualiteit en
steeds met de glimlach. I <3 SAP maar jullie toch nog meer. Bedankt voor al jullie
harde werk, ik apprecieer het enorm.
Acknowledgement
iii
Los van de Labo collega’s, zijn er nog vele andere collega’s die hier verdienen
vermeld te worden. First of all, I would like to thank Leonardo Reyes, partner in
science crime. Both our collaboration in Ghent as our work afterwards have made
me appreciate you as a person, yes, as a friend. I hope that your new life in London
gives you al the (scientific) challenges you are looking for. I would also like to
express my gratitude towards prof. Nadja Nadezhdina and prof. Jan Cermak for the
great week at Obora and for introducing me to the world of sap flow. It is wonderful
that, besides a sometimes different point of view on sap flow methodology, we have
been able to work so well together. Ook prof. Frank Sterck, Paul Copini en Edo
Gerkema van Wageningen UR wil ik bedanken voor de fijne samenwerking
gedurende de MRI meetcampagne.
Dirk De Pauw wil ik enorm bedanken voor alle steun die hij gegeven heeft bij mijn
modelleeravonturen, de software ontwikkeling en de vlotte respons op mijn
suggesties en vragen. Je hebt me in totaal waarschijnlijk meer dan een half jaar tijd
bespaard.
Finally, for the science part, I am most grateful to prof. David Lockington, dr. Adrien
Guyot and the entire MBRS crew for giving me the opportunity to conduct
experiments in the wonderful mangrove ecosystem of Straddie. Adrien and Nina,
thanks for the warm welcome, the help with setting up the sensors and the nice
moments in between it all. I hope you find your way in the future, whether in
Grenoble or still in Brissie with or without the mime guy. Captain Matt, without you
the Belgies would not have been able to work at one of the most beautiful sites in
the world. You brought us there and back safely on your vessel, played Santa
bringing us food and lightened the work with your fine sense of humour. Shark’s
alley will never be the same again, many thanks for all the great Ozzie moments. En
natuurlijk mag ik de Belgies zelf niet vergeten, Michiel, Mieke, Stefanie en Niels, het
was een waar genoegen om jullie ‘meneer den tutor’ te zijn gedurende die twee
maanden.
Maar gelukkig was er naast de wetenschap afgelopen jaren ook nog voldoende tijd
voor zoveel meer. Daarom bedankt aan iedereen die er de laatste jaren buiten het
werk voor me was. Jantje en Sabine, Anneke en Vinnie, Stijntje en Valerie, Cilia en
Charles en Karel en Caroline, tof om te zien dat we na onze gezamenlijke unieftijd
nog steeds samen plezier maken. Ik hoop dat we dat zo kunnen houden en kijk al
Acknowledgement
iv
uit naar wat de toekomst jullie allemaal brengt. Jan, extra bedankt voor de twee
leuke jaren dat we samen op kot zaten en dat je me vorig jaar onder je dak hebt
laten kamperen. Ik zal dan ook mijn uiterste best doen zo goed mogelijk te getuigen
volgende week. Boys, bedankt voor de vele banquets. Binnenkort is het dringend
weer eens mijn beurt. Klaas, ook bedankt voor de hulp met de kolommen in het
prille begin van mijn doctoraat. JNM’ers, jullie zijn met teveel om allemaal
persoonlijk op te noemen. Bedankt voor al die jaren natuur, kampen, activiteiten en
plezier. VP, ik ben blij dat ik een jaar jullie voorzitter mocht zijn, jullie zijn een
fantastische bende! JNM Gent, bedankt om me als West-Vlaming onderdak te bieden,
de vele avonturen waren onvergetelijk. Toch zijn er een paar JNM’ers die ik wel wil
vernoemen. Anton en Pieter (aangevuld door Hanne), jullie zijn de beste huisgenoten
en vrienden die je je kan inbeelden. De cursussen, de activiteiten, de avonden, de
feestjes, de reizen… stuk voor stuk geweldig. Moge er nog veel, veel meer van dat
volgen. Pepijn en Maarten, Spanje en Noorwegen waren overweldigend. Laat het het
begin van een traditie worden. Ik begin alvast een busje te zoeken en wat kano’s op
te blazen. Bart en Pieter, menig vrijdagmiddag hebben jullie me van vertier voorzien,
ik hoop dat ik binnenkort jullie boekske kan lezen. Hetzelfde geldt voor Sam, mijn
bijna-buur en regelmatige passant tussen de bureaus en respectievelijke
koffielokalen. Liezert, bedankt voor de onvergetelijke jaren en voor alles wat je me
geleerd hebt waar een universiteit nooit in zou kunnen slagen. Een vriendschap om
te koesteren.
Ten slotte bedankt aan mijn familie. Broers, eens te meer treed ik in jullie
voetsporen. Ik ken jullie letterlijk mijn hele leven en zou me geen leven zonder jullie
kunnen voorstellen. Na onze jeugd delen we nu ook de rest van het verhaal en daar
ben ik jullie ontzettend dankbaar voor. Jullie hebben me, als grote broers, mee
opgevoed en zo mee mijn leven bepaald. De vele momenten van lol trappen, samen
op stap gaan en elkaar steunen zijn onbeschrijfelijk. Michiel en Eva, bedankt dat ik
altijd jullie deur mag platlopen als ik daar zin in heb, jullie zijn als een tweede
thuis. Kleine Lukas, ik kijk er naar uit om je verder te zien opgroeien en samen
hansje-pansje te verwelkomen. Martijn en Bieke, altijd tof om jullie avonturen uit de
US en nu Zwitserland te lezen. Ondanks de afstand voelt het meteen weer aan als
vroeger als ik jullie in levende lijve zie. Hopelijk kunnen we binnenkort eens samen
de bergen daar trotseren. Pa en ma, de kleinen is nu weer wat groter. Bedankt voor
de gelukzalige, zorgeloze jeugd, de vele kansen, de hulp bij het verbouwen, de nooit
Acknowledgement
v
aflatende steun en het vertrouwen in mijn, soms wat haastige, ondernemingen.
Betere ouders kan je niet dromen. Opa en oma, bedankt voor de mooie momenten
samen, het prachtige voorbeeld dat jullie ons geven en de oprechte interesse in waar
we mee bezig zijn. En dan zijn er natuurlijk nog Rit (toch een beetje een tweede
mama geworden), Simon, Jolijn en Daan. Jullie hebben me meteen laten thuis voelen
daar in de Kempen. Een warm nest waar ik met plezier langskom.
En als laatste is er natuurlijk Celien. Van een wetenschapper wordt verwacht dat hij
wat hij rondom zich ervaart, tracht te begrijpen en verklaren. Maar ik weet dat wat
ik bij jou ervaar, nooit ga kunnen of willen begrijpen, laat staan verklaren. Bedankt
voor de fantastische jaren die we samen al gehad hebben en voor de jaren die nog
komen!
Gent, Mei 2013
vii
Contents
LIST OF ABBREVIATIONS AND SYMBOLS ........................................................... XI INTRODUCTION AND OUTLINE OF THE THESIS ................................................ 1
1 WATER TRANSPORT IN TREES ....................................................... 7
1.1 The driving forces of stem tree water transport and storage ................. 7
1.1.1 Water potential as driving force ............................................................... 8
1.1.2 The cohesion-tension theory ...................................................................10
1.2 Flowing through the tree: the pathways of water ....................................12
1.2.1 Transpiration from the leaves .................................................................12
1.2.2 Water flow in stems ...................................................................................13
1.2.3 Water flow in roots ....................................................................................18
1.3 Taking the other route: hydraulic redistribution .....................................20
1.3.1 Water storage ..............................................................................................20
1.3.2 Hydraulic redistribution ...........................................................................21
1.4 Measuring tree water use variables .............................................................25
1.4.1 Water potential measurements ...............................................................25
1.4.2 Stem diameter fluctuations......................................................................28
2 COMMONLY APPLIED SAP FLOW MEASUREMENT METHODS AND THEIR LIMITATIONS.............................................................. 33
2.1 Introduction ......................................................................................................34
Contents
viii
2.2 Continuous heat sap flux density methods .............................................. 38
2.2.1 Thermal dissipation (TD) method .......................................................... 38
2.2.2 Heat field deformation (HFD) method................................................... 39
2.2.3 Natural temperature gradients ............................................................... 42
2.3 Heat pulse sap flux density methods ......................................................... 43
2.3.1 Compensation Heat Pulse velocity (CHP) method .............................. 44
2.3.2 Tmax method .............................................................................................. 45
2.3.3 Heat Ratio (HR) method ............................................................................ 46
2.3.4 Calibrated Average Gradient (CAG) method ........................................ 48
2.4 Sensor spacing .................................................................................................. 49
2.5 Wounding .......................................................................................................... 50
2.6 General conclusions ........................................................................................ 52
3 ERRONEOUS USE OF THERMAL DIFFUSIVITY IN THE HEAT FIELD DEFORMATION METHOD ................................................... 53
3.1 Introduction ...................................................................................................... 54
3.2 Thermodynamic background HFD method ............................................... 55
3.3 Materials and method ..................................................................................... 58
3.4 Results and discussion ................................................................................... 59
3.4.1 Characteristics of the HFD temperature ratio ..................................... 59
3.4.2 From temperature ratio to sap flux density ........................................ 62
3.5 Conclusions ....................................................................................................... 65
4 THE ANISOTROPIC HEAT CONDUCTION-CONVECTION EQUATION AS BASIS FOR HEAT PULSE SAP FLOW METHODS .
............................................................................................................. 67
4.1 Introduction ...................................................................................................... 68
4.2 Assumption of isotropic medium versus actual anisotropic
sapwood ............................................................................................................. 69
4.3 Implications of anisotropy for current sap flow methods..................... 70
4.4 Towards more accurate equations .............................................................. 77
4.5 Conclusion ......................................................................................................... 78
Contents
ix
5 DIFFERENTIATING BETWEEN BOUND AND UNBOUND WATER IN THE METHOD OF MIXTURES FOR DIFFUSIVITY CALCULATION ................................................................................. 81
5.1 Introduction ......................................................................................................82
5.1.1 But are we missing the point when applying the thermal
diffusivity theory? ......................................................................................85
5.1.2 Corrected equation to determine thermal conductivity Kax..............88
5.2 Materials and Methods ...................................................................................89
5.2.1 Sensitivity analysis .....................................................................................89
5.2.2 Plant material ..............................................................................................90
5.2.3 Thermal conductivity versus water content: original versus
corrected method .......................................................................................90
5.2.4 Implications of the correction for actual
sap flow measurements ............................................................................91
5.3 Results ................................................................................................................92
5.4 Discussion .........................................................................................................97
5.5 Conclusions .................................................................................................... 100
6 DEVELOPMENT OF THE SAPFLOW+ METHOD TO MEASURE SAP FLUX DENSITY AND WATER CONTENT .......................... 101
6.1 Introduction ................................................................................................... 102
6.2 Materials and methods ................................................................................ 104
6.2.1 Theory ........................................................................................................ 104
6.2.2 Water content ........................................................................................... 105
6.2.3 Sensor design ........................................................................................... 105
6.2.4 Identifiability analysis ............................................................................ 107
6.2.5 Comparison of heat pulse methods .................................................... 109
6.2.6 Measurements of sap flux density in artificial sapwood ............... 110
6.2.7 Measurements of sap flux density in sapwood ................................ 111
6.3 Results ............................................................................................................. 113
6.3.1 Identifiability analysis ............................................................................ 113
6.3.2 Sensor verification and calibration ..................................................... 115
6.3.3 Comparison of heat pulse methods by FEM ..................................... 117
6.3.4 Measurements on artificial sapwood .................................................. 120
Contents
x
6.3.5 Measurements on sapwood .................................................................. 121
6.4 Discussion ...................................................................................................... 123
6.4.1 Applicability of the Sapflow+ method ............................................... 123
6.4.2 Comparison of Sapflow+ with other heat pulse methods ............. 126
6.4.3 Challenges for the Sapflow+ method ................................................. 127
6.5 Conclusions .................................................................................................... 128
7 PRACTICAL APPLICATION OF THE SAPFLOW+ METHOD IN MANGROVE WATER RESEARCH .......................................... 131
7.1 Introduction ................................................................................................... 132
7.2 Materials and methods ................................................................................ 134
7.2.1 Field site .................................................................................................... 134
7.2.2 Meteorological data ................................................................................ 135
7.2.3 Ecophysiological measurements .......................................................... 136
7.2.4 Dynamic stem growth model ............................................................... 137
7.3 Applicability of the Sapflow+ method in field conditions .................. 142
7.3.1 Results ....................................................................................................... 142
7.3.2 Discussion ................................................................................................. 144
7.4 Water flow and storage in Avicennia and Rhizophora ......................... 146
7.4.1 Results ....................................................................................................... 146
7.4.2 Discussion ................................................................................................. 156
7.5 Conclusions .................................................................................................... 160
8 GENERAL CONCLUSIONS AND PERSPECTIVES ...................... 163
8.1 Research outcome and scientific contributions .................................... 163
8.2 Future perspectives ...................................................................................... 167
REFERENCES ......................................................................................................... .171 SUMMARY .......................................................................................................... 193 SAMENVATTING ................................................................................................... 196 CURRICULUM VITAE ............................................................................................ 201
xi
List of abbreviations and symbols
Abbreviations
CAG Calibrated Average Gradient
CO2 Carbon dioxide
CHP Compensation Heat Pulse
DOY Day Of the Year
FEM Finite Element Model(ling)
HD Heat Dissipation
HFD Heat Field Deformation
HR Heat Ratio
LVDT Linear Variable Displacement Transducer
MC Water content
MCFSP
Water content at Fibre Saturation Point
MRI Magnetic Resonance Imaging
NaCl Sodium Chloride
NTG Natural Temperature Gradient
RH Relative Humidity
SHB Stem Heat Balance
SPAC Soil Plant Atmosphere Continuum
SF Sap Flow
SFD Sap Flux Density
Abbreviations and symbols
xii
SFDerr
Relative error in Sap Flux Density
TD Thermal Dissipation
TDP Thermal Dissipation Probe
THB Trunk Heat Balance
VPD Vapour Pressure Deficit
WBD Wet Bulb Depression
WSSE Weighted Sum of Squared Errors
2D Two-dimensional
3D Three-dimensional
Latin symbols
A Cross-sectional area
AC Actual soil water conductivity
Astem
Stem cross-sectional area
C Solute concentration
cd Specific heat capacity dry wood
cdw
Specific heat capacity of the woody matrix
cs Specific heat capacity of xylem sap
cw Specific heat capacity of water
D Thermal diffusivity
Din
Inner diameter of the stem segment (without bark)
Dout
Outer diameter of the stem segment (with bark)
d Distance/thickness
e0 Saturated water vapour pressure
e Actual water vapour pressure
Fv Void fraction of the wood
Fv_FSP
Void fraction of the wood at fibre saturation point
g Gravitational acceleration
h Height
k Sensitivity instance
ksoil
Proportionality factor between the soil water potential and the xylem
root water potential
K Thermal conductivity
Kax
Axial thermal conductivity
Abbreviations and symbols
xiii
Kd Thermal conductivity of dry wood
Kd_FSP
Thermal conductivity of wood at fibre saturation point
Krad
Radial thermal conductivity
Ktg Tangential thermal conductivity
Kw Thermal conductivity of water
K Thermal conductivity vector
l Length of the stem segment
L Radial hydraulic conductivity of the virtual membrane separating the
stem storage compartment from the xylem compartment
Lsw
Sapwood depth
M Mass
mw
Molar mass of water
N Number
Neq Osmotic equivalent
P Hydrostatic pressure
Ph Heat input heater needle
q Heat input per unit length of the heater
Q Thermal energy
QT
Temperature to which the amount of heat liberated per unit length of
the line would raise a unit volume of the substance
R Universal gas constant
Rs Resistance
Rs’ Resistance per unit length
Rst Flow resistance between stem xylem and storage compartment
Rx Flow resistance in the stem xylem
r Radius
s Relative sensitivity
∆S Thickness of the storage compartment
t Time
tc
Time after application of the heat pulse at which the temperature at xup
is equal at the temperature at xdown
tm Time at which the temperature at a given distance after application of
a heat pulse is maximal
T Temperature
Abbreviations and symbols
xiv
Tair
Air temperature
Tas Temperature measured in the asymmetric HFD needle
Td Downstream temperature
Tdew
Dew point temperature
Tref
Temperature measured in the axial reference HFD needle
Tstem
Stem temperature
Tu Upstream temperature
∆T Temperature difference
∆Ta Average temperature gradient between the downstream and upstream
temperature
∆T0 Temperature difference at zero flow
∆Tdown
Temperature increase downstream from the heater after application of
a heat pulse
∆Tup
Temperature increase upstream from the heater after application of a
heat pulse
∆Tsym
Temperature difference between the upper and lower axial HFD
needles
∆Tas Temperature difference between the tangential and lower HFD needles
∆Ts-a
Temperature difference between axial downstream and tangential
measurement needle
∆T0(s-a)
Temperature difference between axial downstream and tangential
measurement needle at zero flow
U Voltage
Vh
Heat velocity
Vh_corr
Heat velocity corrected for wounding
Vst Stem storage volume
Vw
Partial molal volume of pure water
wd
Dry weight
wf Fresh weight
Wst Water mass stored in the stem storage compartment
x Axial distance
xup
Upstream axial distance
xdown
Downstream axial distance
y Tangential distance
Abbreviations and symbols
xv
Zax
Distance between the axial HFD needles
Ztg Distance between the tangential and lower axial HFD needles
Greek symbols
Critical value for the pressure component (st
p ) which must be
exceeded to produce (positive) growth in the storage compartment
Collinearity index
δmeas Sensitivity measure
Bulk elastic modulus of living tissue in relation to reversible
dimensional changes (water storage)
0 Proportionality constant
θ Source component value
µw
Chemical water potential
0
wµ Chemical reference water potential
Number Pi
Osmotic pressure
ρc Volumetric heat capacity
ρ Density
ρd Dry wood density
ρs
Sap density
w Density of water
wood Density of dry wood
σ Surface tension at the air-liquid interface
τ Matrix potential
Extensibility of cell walls in relation to non-reversible dimensional
changes (water storage)
Water potential
m Matrix water potential
l Leaf water potential
p Pressure water potential
Osmotic water potential
Abbreviations and symbols
xvi
soil Soil water potential
stem Stem water potential
r Xylem water potential in the roots
x Xylem water potential in the stem
s
p Sap water potential
st
Storage water potential
st
p Storage pressure water potential
st
Storage osmotic water potential
1
4 Introduction and outline of the
thesis
Besides humans, terrestrial plants are the main living organisms influencing the
local and global water cycles. By transpiring, plants take up enormous amounts of
water from the soil and transport these to their leaves, releasing the water as vapour
to the atmosphere. As a mere indication, the total amount of this water transport in
the world’s dense, tropical forests can be up to ~32 x 1015 kg per year (Hetherington
& Woodward, 2003).
The need of water for plant development and growth has led to several branches of
science, many as old as humanity itself. People have known from the very beginning
that in order to obtain vegetable food for human or animal consumption, whether
by gathering or cultivation, water is of crucial importance. During the ages,
strategies to deal with local water scarcity have shifted from a nomadic lifestyle
(Kaniewski et al., 2012), moving to those places where water was in abundance, over
early irrigation channels derived from river beds to wind driven water pumps and,
more recently, highly specialized irrigation techniques based on plant-driven models
(Steppe et al., 2008). Next to water as a resource for plant production, the
importance of plant-water relations has found acceptance in other branches of
science as well, amongst others to investigate colonization by fungi and insects,
fertilization, stress monitoring, reforestation and ecosystem changes. More recently,
the importance of plant water use has also been acknowledged in the global change
concept (Huntington, 2006). Knowing that water vapour has a magnifying effect on
Introduction and outline of the thesis
2
the global temperature change and that more intense drought events can cause
widespread forest decline (Choat et al., 2012), a correct estimation of ecosystem
transpiration is crucial to accurately predict future climate changes and associated
consequences such as civil conflicts (Hsiang et al., 2011). To estimate these
contributions of plant transpiration to global and local water cycles, typically
vegetation models are used (Hanson et al., 2004), whether on the single-plant or the
ecosystem scale.
To understand the hydraulic functioning of plants in relation to the preset research
objectives, measurements of plant water use are essential. Worldwide, sap flow
methods are applied to monitor plant water status and validate vegetation models.
These methods determine flow direction as well as relative and absolute flow,
establishing the link between plant water uptake, release and storage. Hence,
whether it is to assess the correct irrigation dose, to monitor forest vitality or to
obtain trustworthy modelling results, reliable sap flow measurements are
indispensable.
Since the beginning of the previous century when dyes were applied to trace sap
flow in stems and roots (James & Baker, 1933; Dixon, 1936; Kramer, 1940), sap flow
measurement methods have greatly evolved. The application of heat as a tracer has
made sap flow measurements much less destructive and, even though modern
techniques such as Magnetic Resonance Imaging or isotope analysis clearly have
their value in sap flow research, heat-based sensors remain the most practical and
cost-effective option for sap flow assessment. Since the pioneering work of Huber
(1932), a wide range of heat-based sap flow methods have been developed. While all
these methods have their merits and have led to interesting ecophysiological
findings, many methods are limited in the range of sap flow rate or sap flux density
they can measure and are dependent on thermal wood properties or empirical
calibrations. Moreover, wounding and natural temperature gradients can highly
influence the quantitative results. Therefore, the primary objective of this PhD study
was to investigate these limitations and try to come up with possible solutions.
However, before the basic principles of sap flow measurements could be tackled, a
thorough understanding of the mechanisms leading to sap flow had to be acquired.
Chapter 1 describes the driving forces behind plant water uptake and the pathways
water follows on its journey through the plant. Hydraulic redistribution as a way of
Introduction and outline of the thesis
3
water transport going against the expected flow direction is unveiled as a process
following the same fundamentals as common sap flow from soil to atmosphere.
Finally, the main measurable variables describing tree water use are discussed as,
together with sap flow measurements, they form the basics of experimental plant-
water research.
The information on how sap flow in plants can be measured is spread throughout
the scientific literature with most manuscripts focusing on a single method. While
Chapter 1 describes the mechanisms underlying sap flow, Chapter 2 assembles and
critically comments on the current state of knowledge on sap flow measurement
methodology. While sap flow rate methods are briefly mentioned as a means to
determine the integrated flow through the entire plant or stem section in a given
time span (m3 s-1), the chapter mainly zooms in on sap flux density methods,
determining the flow of sap through a certain sapwood area in a given time span (m3
m-2 s-1). The latter leads to a more specific assessment of sap flow on a spatial scale,
enabling more in-depth investigation of ecophysiological traits such as radial and
circumferential variability of sap flow or specific aspects of hydraulic redistribution.
Next to the theoretical background of the existing methods, this chapter also
provides a discussion on the most important factors influencing sap flow methods.
As the only continuous heat based sap flow method encompassing radial sap flow
profiles, high resolution monitoring for both regular and reverse flows as well as
enabling sap flow calculations without the need to assume night-time zero flow
conditions, the Heat Field Deformation method (HFD) (Nadezhdina et al., 2012) has
proven its use in many sap flow studies. However, the underlying methodology is
based on an erroneous use of thermal diffusivity as a sapwood parameter. Chapter
3 explains why thermal diffusivity should not be related to the empirical HFD
temperature ratio and suggests an improved correlation between the latter and sap
flux density, stressing that the HFD method should be considered empirical while
acknowledging its many advantages.
Given the empirical nature of continuous heat based sap flux density methods such
as the HFD, the interest of the scientific community has shifted towards heat pulse
methods as they have a theoretical thermodynamic background. All existing heat
pulse sap flux density methods are founded on the same isotropic heat conduction-
convection equation as mentioned by Marshall (1958). Sapwood, however, is
Introduction and outline of the thesis
4
anisotropic, necessitating an anisotropic theory. This shortcoming in sap flow
method development is addressed in Chapter 4 where the correct basic theory is
derived and the consequences for existing sap flow research are unravelled.
Of the heat pulse methods, the most versatile is no doubt the Heat Ratio method
(Burgess et al., 2001a). Although limited for high flows, this method enables
measurements of average, low as well as reverse flows, converting the measured
temperature ratios to sap flux density based on the axial thermal diffusivity of the
sapwood. The latter is determined during zero flow conditions, based on a method
of mixtures applied to a sapwood sample cored from the tree. In this method of
mixtures, however, the meaning of the water content is misinterpreted, leading to
incorrect diffusivity calculations. Chapter 5 proposes a correction to this method,
including the proper incorporation of sapwood water content.
Given the limitations of existing sap flux density methods, the urge arose to search
for alternatives. Chapter 6 tries to tackle these limitations by presenting a new sap
flux density method, the Sapflow+ method, enabling sap flux density measurements
independent of thermal diffusivity determination across the entire naturally
occurring range of sap flows. Moreover, this method holds the promise of
simultaneously determining stem water content.
After the theoretical development of the Sapflow+ method and the confirmation of
its applicability by lab tests, Chapter 7 presents how the Sapflow+ method can be
applied in harsh field conditions to study tree water use. An experiment was set up
in on North Stradbroke Island, Australia to assess water use of Avicennia and
Rhizophora, two dominant mangrove species. By measuring stem diameter
variations, water potentials and sap flux density, the differences in water use of
these co-occurring species coping with the challenging environmental conditions
were revealed.
Finally, Chapter 8 summarizes the main findings of this PhD study and formulates
their implications and challenges for ongoing and future research. It is discussed
which questions remain unanswered and where promising areas of future research
lie.
Introduction and outline of the thesis
5
In summary, this PhD thesis addresses the following main questions:
- Which current methods are available to determine sap flow in plants?
- On which basis are these methods found?
- What are the differences between these methods and their limitations?
- How can sap flow measurements still be improved?
7
1 1 Water transport in trees
Trees are sanctuaries. Whoever knows how to speak to them, whoever knows
how to listen to them, can learn the truth. They do not preach learning and
precepts, they preach, undeterred by particulars, the ancient law of life.
Hermann Hesse, Bäume. Betrachtungen und Gedichte
1.1 The driving forces of stem tree water transport and
storage
The question of how large trees such as redwoods can transport water over
distances more than 100 m has fascinated man since centuries. Thorough research
has led to the general acceptance that water moves through plants in a passive way,
driven by differences in water potential according to the cohesion-tension theory
(Dixon & Joly, 1894; Slatyer, 1967; Tyree & Zimmerman, 2002).
Chapter 1
8
1.1.1 Water potential as driving force
Water moves passively from a higher to a lower chemical water potential. This
chemical water potential (µw in J mol-1), corresponding to the free energy of water,
can be expressed as:
Π τ0
w w w w w wµ =µ -V +V P-V +m g h (1.1)
with 0
wµ the chemical potential of pure water for a specific reference state, Vw the
partial molal volume of pure water (18.0×10-6 m3 mol-1), Π the osmotic pressure (Pa)
caused by the attraction of water by dissolved solutes, P the hydrostatic pressure
(Pa), τ the matrix potential caused by capillary forces (Pa) and mw g h the term
describing the influence of gravity with mw the molar mass of water (kg mol-1), g the
gravitational acceleration (9.81 m s-2) and h the vertical height compared to the
reference state (m).
The difference between µw and the reference state 0
wµ represents the amount of
work needed to move one mole of water from the reference to the actual level of
chemical water potential with the reference defined as pure water at atmospheric
pressure, at zero height level and at the same temperature as the considered
system. When diverting from this reference state, the water is not in equilibrium and
tends to passively flow towards a location where the difference with the reference
state is lower.
Although explaining passive water flow, the concept of chemical water potential is
not very practical as chemical potentials are difficult to measure in field conditions.
Therefore, plant physiologists prefer to work with water potentials ( ), expressed
in pressure units (Pa, or more commonly MPa) and obtained by dividing the
chemical potential by Vw:
τ
0
w ww
w
µ µP- + g h
V (1.2)
with ρw the density of water (kg m-3). As both V
w and 0
wµ are constants, water will
passively flow from a higher (less negative) to a lower (more negative) water
potential . This water potential can be divided in different components:
Water transport in trees
9
The pressure potential p (= P), indicating the physical pressure on the
water, which can be either positive or negative.
The negative matrix potential m (=- τ ), representing the interactions
between the water and air in numerous capillary interstices in plant tissues
or soils due to the attraction between water and hydrophilic surfaces. Notice
that m and p are mostly considered as one, describing the hydrostatic
pressure which can be positive when water exerts pressure against the cell
wall (turgor) or negative when water is under tension as in the xylem
elements (see Section 0). Throughout this thesis, pressure potential p will
include the matrix potential.
The negative osmotic potential
(=- ) due to the presence of dissolved
solutes as water tends to be transferred from a lower to a higher
concentration of solutes across a semipermeable membrane.
can be
determined according to the Van ‘t Hoff’s equation:
- -RT C
(1.3)
with R the universal gas constant (8.31 J mol-1 K-1), C the solute concentration
(mol m-3) and T the solution temperature (K). Hence, the higher the solute
concentration, the more negative
.
The positive gravitational potential g (= w g h ), related to the gravitational
forces exerted on the water at a certain height h. This potential is only taken
into account for tall trees.
This water potential concept is applicable for water in the liquid phase throughout
the soil-plant-atmosphere continuum (SPAC). For water in the vapour phase, at the
boundary of leaf and atmosphere level, is expressed by the Spanner equation
(Spanner, 1951a):
0
w
R T eln
V e (1.4)
Chapter 1
10
where R is again the universal gas constant (8.31 J mol-1 K-1), T the absolute
temperature (K) and e0 and e the saturated and actual water vapour pressure (Pa),
respectively.
Even though the concept of water potentials explains the transport of water from a
higher (less negative) to a lower (more negative) water potential, it does not indicate
how these water potentials are created within the tree. To this end, the cohesion-
tension theory was developed (Dixon & Joly, 1894; Tyree, 1997).
1.1.2 The cohesion-tension theory
The cohesion-tension theory states that water inside the apoplast of trees, the cell
wall continuum of a plant containing the dead conductive xylem cells, forms a
continuous string thanks to the cohesion forces between water molecules, caused by
hydrogen bonds. If then at one end of this string the water is being attracted
because of a lower water potential, the water molecules will resist to be pulled apart
and a tension will be propagated within the water string. This cohesiveness of water
molecules, together with the adhesive forces between water molecules and the walls
of xylem elements, allows water to be transported within the stem.
But what induces these lower water potentials, creating the attractive forces on
these water strings, causing them to be under tension? As the gravitational potential
is always positive, it can be ruled out. Hence, these forces must be caused by
changes in pressure and/or osmotic potential. The most influential cause of a
decreasing pressure potential leading to upward sap flow is transpiration. This
process comprises the water loss from leaves to the atmosphere, pulling up the
water strings through all components of the SPAC (see section 1.2). Within the
leaves, a meshwork of small interstices exists, created by the cellulose microfibrils
in the cell walls. These interstices act as a fine capillary network where water is in
contact with the air. Because of the strong adhesion between water and these cell
walls, many curvatures (menisci) are formed, inducing a negative pressure potential
in the sap directly behind the menisci (Nobel, 1999):
2s
p r
(1.5)
where σ is the surface tension at the air-liquid interface (0.0728 N m-1 at 20°C) and r
is the radius (m) of the meniscus, which is by convention positive for a concave
Water transport in trees
11
surface. As during transpiration water evaporates into the inter-cellular spaces of
the leaf, this radius r decreases, causing the pressure potential to become more
negative and, hence, creating a tension in the water string.
Next to transpiration, other processes can induce tension in the water column,
causing water to move downwards within the SPAC or even in opposite directions
within the tree. This phenomenon is termed hydraulic redistribution and is the
subject of Section 1.3.
As according to the cohesion-tension theory strong negative pressures are induced,
the water column will be in a highly metastable state. For over a century, this has
led the cohesion-tension theory to be subject to criticism (Zimmermann et al., 1994;
Canny, 1995; Zimmermann et al., 2004), leading to alternative theories explaining
sap flow in plants. Canny (1995) developed the compensating pressure theory,
stating that the tension in the water column due to transpiration is compensated by
the pressure exerted by the surrounding tissues, protecting the water from going
into the metastable state. This theory, however, has been widely disputed in a series
of meticulous studies and has never been proved by experimental data (Stiller &
Sperry, 1999; Tyree & Zimmerman, 2002). More recently, Zimmerman et al. (2004)
roused the debate again, stating that ‘negative xylem pressure values of several
megapascals exist only in the realm of science fiction’. These authors argue that
water in tall trees moves in analogy to the lifting of ships by consecutive watergates
thanks to occasional axial barriers or adherence to gel matrices. Their main
argument against strong negative xylem pressures seems to be the possible errors
induced by pressure bomb measurements (Scholander et al., 1965). Similar negative
pressures have, however, been measured independently by applying centrifugal
forces or stem psychrometers (Dixon & Tyree, 1984; Holbrook et al., 1995).
Moreover, the statements of Zimmerman et al. (2004) were immediately countered
in a commentary of Angeles et al. (2004), subscribed by over forty international
experts in tree water relations, stating that the work of Zimmerman et al. (2004) is
misleading in its discussion on the fundamentals of the cohesion-tension theory and
that the latter is widely supported as the only theory consistent with the enormous
amount of data on water transport in plants. Therefore, this theory will also be
accepted as correct throughout this study.
Chapter 1
12
1.2 Flowing through the tree: the pathways of water
From all the water taken up by the roots, 95% or more leaves the tree again through
transpiration (Ridge, 2002). This water loss can be seen as a side effect of
photosynthesis, the process converting the energy of the sun into sugars, the basic
building components of plants. Nevertheless, this water flow is of crucial
importance as it transports mineral nutrients from the soil to the leaves and cools
down these leaves as protection against high solar radiation. Moreover, without the
positive pressure that water exerts on cell walls (referred to as turgor pressure),
plants would not be able to grow. The following sections describe the different cell
types and tissues water encounters on its way through the plant.
1.2.1 Transpiration from the leaves
While water transport in trees is often described as starting at the roots, it is the
water loss from the leaves that induces flow. Imagine a healthy tree before sunrise,
its different flow paths filled with water. When the sun rises, the leaves’ stomata
open, allowing the diffusion of CO2 in the substomatal cavities to enable
photosynthesis (Figure 1.1). However, as the water potential of the atmosphere is
highly negative according to the Spanner equation (Eq. 1.4), water vapour from the
substomatal cavities and intercellular air spaces will be drawn away through the
stomata. This induces evaporation of water from the surface of the mesophyll cells,
reducing the menisci of water-air interfaces and, hence, lowering the water potential
(Section 1.1.2). Because of this lowered water potential, water is transported from
the xylem in the vascular bundles to the mesophyll cells, further propagating
tension throughout the water conducting system in the stem and roots.
Next to stomatal transpiration, water may also diffuse across the cuticle (cuticular
transpiration) (Jones, 1992). The resistance to evaporation through the cuticle,
which is not adjustable by the plant on the short-term and predominantly
dependent on the thickness of the cuticle, is, however, much larger than the
stomatal resistance. Moreover, the latter can be actively regulated by the plant as a
response to internal factors, such as the internal CO2, or external conditions, such as
light, temperature, relative air humidity and soil water availability. Hence, unless
stomata are (nearly) closed, cuticular transpiration only accounts for a small
percentage in leaf water loss (Nobel, 1999; Phillips et al., 2010; Zeppel et al., 2010).
Water transport in trees
13
Cuticle
Upper epidermis
Pallisade
mesophyll cell
Spongy
mesophyll cell
Air space
Vascular
bundle
Stomatal pore
Guard cellLower
epidermisCuticle
1.2.1 Water flow in stems
The water drawn from the leaves induces tension which propagates throughout the
water conducting elements in the stem, called xylem (Figure 1.2). Together with the
photosynthate-conducting tissue, indicated as phloem, the xylem makes up the
vascular system which can be found in the entire tree, from root to leaves. Both of
these transport tissues are produced by the vascular cambium, differentiating
secondary phloem outwards to the bark and secondary xylem inwards. While the
phloem mainly consists of living tissue, transporting photosynthesis products from
sources to sinks throughout the plant, xylem mainly comprises dead cells. These
cells do not only serve as water conducting pathways, they also provide structural
support for non-woody plants and young trees. For older trees, this support
function is taken over by the non-conducting heartwood, generated from the inner
part of the xylem which has lost its conducting function over time (Raven et al.,
1992).
Figure 1.1 Schematic transverse leaf section, indicating the various cell types. The blue arrows
indicate the diffusion of water to the atmosphere via the stomata, inducing water flow from
the vascular bundle, while the red arrows represent the uptake of CO2 (adapted from
http://glencoe.MCgraw-hill.com/sites/0078759864/student_view0/unit6/chapter22/
standardized_test_practice.html)
Chapter 1
14
Ψsoil = -
0.3 MPa
Ψstem =
-0.8 MPa
Ψroots =
-0.6 MPa
Ψleaves =
-1.0 MPa
Ψair =
-100.0 MPa
Xylem sap
Mesophyll cells
Stomata
Water molecules
AtmosphereTranspiration
Cohesion and
adhesion in the
xylem
Water uptake
from the soil
Adhesion by
hdydrogen
bounding
Cell wallXylem cells
Cohesion by
hdydrogen
bounding
Water molecules
Root hair
Soil particle
Water
Wa
ter
po
ten
tia
l g
rad
ien
t
Xylem flow
Within the xylem, a distinction can be made between vessel elements (only found in
angiosperms) or the more primitive tracheids (found in angiosperms, gymnosperms
and the lower vascular plants) (Figure 1.3a). For both types, conducting elements are
axially arranged end-to-end. However, whereas tracheids typically have tapered
ends, the generally shorter and broader vessel elements are adjoined by blunt ends.
The cell wall of these ends are distinctively perforated (hence the name perforation
plates), reducing the axial resistance within the vessel network, providing a suited
pathway for water transport. Tracheids, on the other hand, do not contain
Figure 1.2 A schematic representation of water movement through the SPAC. Removed from
the leaves by transpiration, water is sucked up from the roots, following the gradient in water
potential, created according to the cohesion-tension theory (adapted from Campell & Reece,
2008).
Water transport in trees
15
perforation plates, forcing the water to flow through much smaller holes in their
touching boundaries, creating a higher axial resistance towards water flow
(Pittermann, 2010).
Vessels Tracheids
Perforation
plates
Pits
(a) (b)
Next to axial transport, water can also flow laterally between xylem cells. The thick
lateral secondary walls of these cells, which makes xylem very inelastic, are
punctured with small pits (Figure 1.3a). These pits, only existing of a very thin and
porous primary cell wall, allow the free passage of water and nutrients while
limiting the passage of air, pathogens and particles (Choat et al., 2003). Via the pits,
xylem elements are integrated into a complex network, giving the water the
necessary flexibility of altering its flow path in case water conductance through
certain cells fails. As water under tension in the xylem is in a metastable state, little
stress is needed to induce air bubble formation in the conducting cells (cavitation).
If then the tension of the xylem sap decreases below a certain threshold value, air
from cavitated vessels will penetrate the largest pit membranes, filling the adjacent
vessels, a process known as ‘air seeding’. As these vessels cease to function, the
water has to find another way upwards. As for other pits the cavitation threshold
will be higher (a more negative water potential), the water can relocate through
Figure 1.3 (a) The different water conducting cell types in the secondary xylem of trees:
vessels and tracheids (adapted from Campbell et al., 2004); and (b) structure and composition
of a woody angiosperm stem section (adapted from Raven et al. (1992))
Chapter 1
16
these pits to those cells that still hold their conductive capacities. If, however, the
tension further increases due to extended stress, too many xylem elements may
become cavitated, blocking upwards sap flow and finally resulting in plant wilting.
Next to vessel elements and tracheids, the xylem system also comprises fibres and
parenchyma cells. The latter are, in contrast with the conductive elements, living
cells which form xylem rays (Figure 1.3b) facilitating lateral movement of water and
solutes into and out of the conducting cells. Moreover, these cells form storage
compartments for carbohydrates. Xylem fibres, on the other hand, are slender,
lignified cells offering structural support to the xylem.
Secondary xylem is generally not uniformly produced throughout the year (Gricar,
2010). The cyclic pattern of seasonal cambial activity leads to a distinction in early
wood, with typically less dense and wider vessels, produced at the beginning of the
growing season, and late wood, which is produced at the end of the growing season
and typically contains denser and narrower vessels. While for some species, there is
hardly any structural difference between early wood and late wood (the so called
diffuse porous species), for others the distinction is clear, enhancing the visibility of
the growth rings (the so called ring porous species) (Butterfield & Meylan, 1980). It
should, however, be noticed that the distinction between early and late wood is not
only species, but also environmentally dependent as it has been shown that
different trees from the same species may or may not show large differences
between early and late wood based on seasonal intensity (Robert et al., 2011b).
Diffuse and ring porous species are often grouped together, forming the hardwoods
of angiosperms, while the wood of gymnosperms is frequently referred to as
softwood or coniferous wood. The latter also may or may not show clear
distinctions between early and late wood depending on species and environmental
conditions.
Phloem flow
While the transport of water and nutrients takes place in the xylem, water-dissolved
photoassimilates are conducted via the phloem. This plant tissue consists of two
cell types: sieve elements and companion cells (Figure 1.4a) (Taiz & Zeiger, 2006). In
gymnosperms and lower vascular plants, the sieve elements (sieve cells) are
generally longer, less wide and more tapered than the sieve tube elements found in
angiosperms. Both sieve elements lose their nucleus, tonoplast (and thus their
Water transport in trees
17
vacuole), Golgi bodies and ribosomes as they mature. Nevertheless, the cytoplasm,
cell membrane, endoplasmatic reticulum, few mitochondria and phloem-specific
proteins and plastids remain. Therefore, these elements are still considered as living
cells (Knoblauch & Peters, 2010). To metabolically sustain these sieve elements, they
are neighboured by specialized cells, called albuminous cells in gymnosperms and
companion cells in angiosperms. These cells do have nuclei and generally hold many
mitochondria, providing energy to the sieve elements. Besides, these neighbouring
cells are connected to the sieve elements by plasmodesmata, allowing transport of
solutes to and from the sieve elements.
Transport of phloem sap is facilitated by the sieve plate, the end-to-end connection
between sieve-tube elements, grouping them in sieve tubes. This sieve plate consists
of clusters of pores through which the protoplasts of adjacent sieve-tube elements
are connected. Therefore, phloem sap moving through the sieve tube does not need
to cross cell membranes.
Next to sieve elements and their accompanying cells, phloem also comprises
parenchyma cells, with storage as their primary goal, and fibres (sometimes
sclereids), giving strength to the tissue. In contrast to xylem cells, phloem cells are
never lignified, making the phloem tissue much more elastic.
A C
B
D
Sieve plate
Companion
cell
Sieve-tube
elements
Plasmodesma
Sieve
plate
Nucleus of
companion
cell
Fibers
(a) (b) (c)Sieve-tube
elements
Plasmodesmata
Sieve plate
Companion
cell with
nucleus
Xylem Phloem Cambium
In angiosperm trees, the phloem is mostly situated in the bark, separated from the
xylem by the vascular cambium (Figure 1.3b). Besides the phloem, the bark also
consists of the periderm and cortex, forming the outermost tissues of the stem. Not
Figure 1.4 (a) Longitudinal view of phloem tissue, including sieve tube elements and
companion cells (Campbell et al., 2004); (b) successive cambia organised in concentric
cylinders; and (c) successive cambia organised in a reticulate network (adapted from Robert et
al. (2011a))
Chapter 1
18
all species show this clear boundary between phloem at the outer part and xylem
more centrally in the stem. While girth expansion in vascular plants is generally the
result of the meristematic activity of one cylindrical vascular cambium, some
species produce several successive cambia (Figure 1.4b) (Carlquist, 2007). These
cambia can literally develop successively although also simultaneous development
is possible (Schmitz et al., 2008). Next to this concentric organisation of successive
cambia, some species such as Avicennia have shown an intricate three-dimensional
network of cambia, resulting in a patchy growth pattern where active growth
displaces around the stem circumference with time (Schmitz et al., 2008; Robert et
al., 2011a).
While the transport of water and nutrients in the xylem is tension driven, the flow of
phloem sap is determined by sink-source interactions according to the pressure-
flow hypothesis (Münch, 1930). This hypothesis states that the flow in the phloem
tissue is driven by an osmotically generated pressure gradient between sources and
sinks. As at the source level photoassimilates are actively or passively transported
in the phloem, the osmotic potential is lowered, attracting water from the
surrounding tissues such as the xylem cells. This added water increases the
hydrostatic potential of the phloem cells (turgor). At the sink level, these
photoassimilates are unloaded from the phloem, decreasing its osmotic potential in
the phloem and forcing water towards the sinks. The pressure difference which is
thus created, sustains the flow from sources to sinks throughout the tree. This flow
is further aided by apoplastic loading steps between the sieve tubes, acting as relays
throughout the flow pathway (Lang, 1979; Knoblauch & Peters, 2010). As source
unloading in the phloem leads to water attraction from the xylem, an additional
tension in the xylem sap is created, causing the so called ‘Münch’s counterflow’.
This upwards xylem flow occurs even in the absence of transpiration to sustain the
water recycling in the phloem tissue (Windt et al., 2006; De Schepper & Steppe,
2010).
1.2.2 Water flow in roots
From the stem, xylem elements continue in the roots. If water is drawn upwards
during transpiration, the tension in the root xylem will rise, attracting water from
the soil through the root system.
Water transport in trees
19
Root hairs, which are fine extensions of the epidermal cells, ensure a large contact
surface with the surrounding soil, facilitating water uptake. After an easy passage
through the single-cell layer of the root epidermis, waters moves through the root
cortex via two dominant pathways: the apoplast and the symplast (Figure 1.5).
During the apoplastic pathway, water moves within the continuum of cell walls and
extra-cellular spaces outside living cells while for the symplastic pathway it moves
within the protoplasm of the cells, connected by narrow plasmodesmata. A third,
less common, pathway consists of the non-plasmodesmic water transport between
cells, requiring the water to cross the cell membranes when entering and leaving the
cells (Taiz & Zeiger, 2006).
To travel from the cortex to the apoplastic xylem in the stele, water is forced to
cross the endodermis. This tissue consists of a single layer of cells of which the
anticlinal walls are impregnated with waxy materials such as suberin and lignin and
form the Casparian strip. Because of its composition, this waterproof Casparian
strip does not allow apoplastic transport, forcing the water to take the symplastic
pathway, a unique feature in the tree water transport system. This forced symplastic
transport has several implications (Tyerman et al., 2002). It does not only prevent
water loss through the roots in case of extreme drought events, it also enables the
roots to actively regulate their hydraulic conductivity by adapting the abundance
and permeability of aquaporins (water transporting proteins). Besides, the Casparian
strip allows accumulation of solutes in the xylem during conditions of high soil
water availability and low transpiration rates. As this increased solute concentration
will lower the osmotic potential, water will be attracted towards the root xylem
across the symplastic membranes, causing a positive hydrostatic pressure. This
‘root pressure’ has been attributed to rehydrate embolized xylem conduits and
allow the relocation of nutrients (Pickard, 2003; Clearwater et al., 2007). A typical
example of root pressure is the leakage of sugary xylem sap from damaged stems at
the beginning of spring, when root reserves are remobilized before budburst.
Chapter 1
20
Symplastic
pathway
Apoplastic
pathway
Root hair
Epidermis
Cortex
Endodermis Stele
Xylem
vessels
Plasma
membrane
Casparian strip
Symplastic
pathway
Apoplastic
pathway
Casparian strip
Endodermal cell
1.3 Taking the other route: hydraulic redistribution
In the previous sections, the upwards xylem flow, induced by transpiration at the
leaves, was used as an example to understand the cohesion-tension theory and to
present the different water conducting plant tissues. Water, however, is not solely
transported from roots to leaves as water uptake and release are dynamic
processes, including storage and redistribution phenomena.
1.3.1 Water storage
Generally, a time lag can be noticed between the transpiration at leaf level and the
water uptake by the root system. As water is transpired from the leaves, tension is
created throughout the xylem sap, pulling the water upwards. Because of the
hydraulic resistance between leaves and roots, the amount of water taken up by the
root system cannot immediately fulfil the demand of water at the leaves. To meet
this shortage, water is released from the different storage compartment located
Figure 1.5 A schematic representation of the water pathways inside the roots, focussing on
the role of the Casparian strips (source: http://www.nicerweb.com/bio1152/Locked/
media/ch36/root_transport.html).
Water transport in trees
21
throughout the tree (Sevanto et al., 2002; Steppe et al., 2006; De Schepper & Steppe,
2010). On the other hand, when transpiration decreases, the water potential in the
xylem increases, inducing water flow from the xylem back to the surrounding
storage compartments. According to Tyree & Zimmerman (2002), three different
mechanisms of water storage can be distinguished.
Living cells form the first storage compartment, consisting of elastic cells
which are in the stem mainly located in the bark (phloem, cambium and
parenchyma) and the wood rays (Zweifel et al., 2000). Changes in water
content of these elastic tissues are accompanied by volume changes, visible
as shrinking and swelling of the stem. As long as the cells are not damaged,
this storage process is reversible.
The second storage compartment is formed by the capillaries in the lumens
of inactive xylem elements and intercellular spaces of the active xylem
tissues. This capillary water is almost entirely released if the water potential
lowers beneath -0.5 MPa (Tyree & Ewers, 1991). This process is also reversible.
A final storage mechanism is the release of water due to cavitation. This
threshold at which this water release occurs is dependent on the diameter of
the intervessel pits, ranging from -0.5 MPa for some species to -5 MPa or
more for others (Tyree & Ewers, 1991).
1.3.2 Hydraulic redistribution
Next to transport to and from the storage tissues, xylem sap can also be relocated
within the xylem. This phenomenon is generally referred to as ‘hydraulic
redistribution’ (Nadezhdina et al., 2010) and is a passive movement of water,
controlled by competing soil and plant water potential gradients and corresponding
pathway resistances (Nadezhdina et al., 2009).
Many studies have shown that water can transfer passively from moist to drier
portions of the soil profile via roots (Burgess et al., 1998; Meinzer et al., 2004;
Oliveira et al., 2005; Brooks et al., 2006; Howard et al., 2009; Domec et al., 2010;
Prieto et al., 2011). Depending on the flow direction of the water in the soil, three
types of hydraulic redistribution are distinguished (Figure 1.6). The term ‘hydraulic
lift’ describes the upward movement of water from deep wet to shallow dry soil
layers (Figure 1.6a), while the reverse movement from shallow to deeper soil is
Chapter 1
22
sometimes referred to as ‘downward hydraulic redistribution’ (Figure 1.6c). Next to
these vertical flows, water may also be transported laterally (lateral redistribution,
Figure 1.6b) from moist to drier soil patches. This redistribution of water in the soil
helps to maintain the soil water content in a range that prevents the soil water
potential from dropping to the critical threshold that would cause root hydraulic
failure due to cavitation (Domec et al., 2004; Warren et al., 2007; Siqueira et al.,
2009). As hydraulic redistribution in the soil accounts for more than 20% of the
water taken up during transpiration, it even affects land-surface climatology (Brooks
et al., 2002; Lee et al., 2005).
(a) (b) (c)
Figure 1.6 Scheme of the different types of hydraulic redistribution in the soil compartment.
(a) Hydraulic lift; (b) Lateral redistribution; and (c) Downward hydraulic redistribution.
Different sizes indicate different water potentials: the bigger the symbol, the higher (less
negative) the water potential. Arrows indicate the flow direction. Adapted from Nadezhdina et
al. (2010).
Water transport in trees
23
Hydraulic redistribution, however, does not only take place in the roots. Stephen
Hales (1727) conducted an experiment almost 300 years ago, providing evidence of
the possibility of reverse flow in tree stems (Figure 1.7).
(a) (b)
This reverse flow can be the result of several different processes, again passively
driven by water potential gradients (Figure 1.8). Canopy water uptake occurs when
water absorbed by leaves during rain, fog or dew events is transported from the wet
foliage to the dryer stem, root or soil compartments (Figure 1.8a). This foliar
absorption of water has shown to play a significant role in the water balance of
many ecosystems during drought events (Yates & Hutley, 1995; Burgess & Dawson,
2004; Breshears et al., 2008; Limm et al., 2009; Simonin et al., 2009). Next to water
uptake, water can also be redistributed within the tree. During moments of low
transpiration because of stomatal closure, whether at night or during conditions of
very high vapour pressure deficits (VPD) at daytime, water can move from the
different storage tissues to those compartments where water potential is highly
negative (Figure 1.8b). This ‘tissue dehydration’ occurs mainly under extreme and
prolonged drought conditions, when soil water potential drops below leaf water
potential (Nadezhdina et al., 2010).
While soil moisture measurements, water potential determination and isotope
analysis can indicate general flow directions and, hence, point to hydraulic
Figure 1.7 Illustration of the experiment conducted by Hales (1727) showing the water flow in
a large branch of an apple tree. The flow changed from roots (1)-leaves (2) direction during
transpiration (a) to the leaves (2)-roots (1) direction after branch severing when its cut upper
tip was put into water (b) (Nadezhdina et al., 2009).
Chapter 1
24
redistribution, it was not until the use of sap flow methods allowing bi-directional
flux measurements that the true complexity of this phenomenon could be assessed.
Nadezhdina et al. (2009) conducted a field experiment in which part of the roots
were located in drier soil while the opposite roots were adequately wetted. By
applying HFD sap flow sensors, it could be seen that water was taken up from the
wetted roots and then transported upwards in the stem before reversing to meet the
dry soil of the opposite roots during night (Figure 1.8c). Moreover, while the inner
xylem of the dry roots was conducting water to the soil, the outer xylem conducted
water back upwards. This simultaneous occurrence of both regular and reverse flow
points to radial sectoring, a feature which also has been noticed without hydraulic
redistribution events (Orians et al., 2004; David et al., 2012).
(a) (b) (c)
Even though hydraulic redistribution is becoming an increasingly important feature
in hydrodynamic plant research, many questions remain unresolved. To further
improve our understanding of this phenomenon and allow its integration in plant
water use models, reliable measurements of tree water use variables are essential.
The next and final section of this introductory chapter will discuss the most
important methods to determine plant water use variables before focussing on the
main subject of this study: sap flow measurements.
Figure 1.8 Scheme of the different types of hydraulic redistribution in the below-ground tree
compartments: (a) canopy wetting by rain, fog or dew increases the water potential to nearly
zero, stimulating reverse flow to the stem and roots; (b) in cases of severe drought, water from
internal storage can flow downwards if transpiration is low; and (c) water being redistributed
in the stem following water potential gradients via the path of lowest resistance, allowing both
upward and downward flow in the same transversal stem section (adapted from Nadezhdina
et al. (2009)).
Water transport in trees
25
1.4 Measuring tree water use variables
‘The numbers tell the tale’ is a commonly heard expression in science, indicating
that hypotheses and theories need to be sustained by factual measurements. It is
obvious that fundamental concepts such as the cohesion-tension theory or hydraulic
redistribution could only have been developed thanks to measurement methods
allowing the assessment of a wide range of tree water use variables. This section
briefly describes the most common methods to determine water potentials
throughout the SPAC and to assess stem diameter changes, together with sap flow
the most important variables in plant water use research.
1.4.1 Water potential measurements
Soil water potential
Soil matrix water potential is measured either by measuring properties of the soil
which change with the water potential such as water content, electromagnetic
radiation, infrared reflectance, thermal or electrical conductivity or by equilibrating
the liquid or gas phase of the water in some reference medium with the liquid phase
of the soil (Campbell, 1988). The most commonly applied method to determine soil
matrix potential in-situ is probably tensiometry. Tensiometers exist of a porous cup,
connected to a tube filled with de-ionised water (Sormail & Vachaud, 1969). At the
top of this tube, a pressure transducer registers pressure changes above the water-
air meniscus in the tube. As the cup is placed firmly in contact with the soil, the
water inside the tensiometer will equilibrate with the soil water over the porous
ceramic cup. When properly calibrated by means of a pressure calibrator, this
simple method directly and continuously allows the determination of soil water
matrix potentials. If, however, the surrounding soil becomes to dry, air will be able
to enter the ceramic cup, distorting the tensiometer readings. Moreover, at low
water potentials, water will start to evaporate inside the tube, causing cavitation
inside the instrument. Therefore, tensiometers are limited to water potentials within
the approximate range of 0 to -0.1 MPa, although equitensiometers are able to
measure more negative water potentials.
A method to assess soil water potential as combination of matrix and osmotic
potential is soil psychrometry. Based on the work of Hill (1930) and Spanner
(1951b), Monteith & Owen (1958) employed the Peltier effect in their thermocouple
Chapter 1
26
psychrometer design to measure the total suction of soil water. To this end, a fresh
soil sample is placed in a small chamber with a high thermal mass. Within this
chamber, the sample is left to equilibrate to ensure that the water potential of the
air in the chamber is in equilibrium with the water potential of the soil sample. After
equilibration, a small current is sent through the copper-constantan thermocouple
located in the chamber above the soil sample. This Peltier current will cause the
thermocouple to cool down below the dew point, inducing a water droplet to form
on its surface. Then, the Peltier current is switched off and the thermocouple
temperature rises again, causing a measurable voltage different because of the
Seebeck effect. During the evaporation of the droplet, the temperature of the
thermocouple stays constant, forming a plateau in the voltage readout. When the
droplet is completely evaporated, the temperature further increases until it is again
at its original value. This process results in a typical psychrometer output (Figure
1.9) in which the wet bulb depression (WBD) indicates the voltage difference
between the output during evaporation of the droplet and the reference output. This
WBD can be linearly related to the water potential based on a calibration of the
psychrometer with NaCl solutions of which the water potentials are known.
Time after cooling (s)
0 10 20 30 40 50 60 70
Voltage (
mV
)
0
5
10
15
20
25
30
WBD
Figure 1.9 Typical psychrometer output showing the voltage signal over time after the cooling
of the thermocouple. The voltage difference between the evaporation output and the reference
signal is indicated as the wet bulb depression (WBD) and is proportional to the water potential
of the soil sample.
Water transport in trees
27
The soil psychrometer as described above has a major practical limitation. Because
of the need for stable temperature conditions and the insertions of soil sample in
the psychrometer chamber, the method is limited to laboratory research (Monteith &
Owen, 1958). Recently, however, soil psychrometers have been developed that allow
on-site measurements. These have the minor disadvantage that they cannot be used
in completely saturated soils and can only measure at sufficiently large depths in
order to reach thermal equilibrium of the small psychrometer chambers.
Stem water potential
Similarly as for soil water potential measurements, the psychrometer principle can
be applied to determine stem water potential. It was, however, not until the work of
Dixon & Tyree (1984) that a practically applicable stem psychrometer was
developed. These authors attached a small chamber holding two thermocouples to
the sapwood after cutting away the bark. One of the thermocouples touches the
sapwood while the other measures the temperature in the chamber, allowing
measurement of and correction for the temperature gradient between the sample
and the dew point measuring junction.
Leaf water potential
While leaf water potential can be measured with leaf psychrometers as well, this
technique is less practical as a psychrometer chamber is much more difficult to
properly attach on a leaf surface compared to a stem surface. Moreover, leaves are
more prone to temperature changes which may influence the measurements. The
more traditional device for measuring leaf or twig water potentials is the Scholander
pressure bomb (Scholander et al., 1965). This method is based on the fact that, when
a leaf petiole or twig is cut, the xylem sap, which was under tension before cutting,
will recede into the xylem below the cut surface. If then the leaf or twig is placed
upside down in the chamber of the pressure bomb, a positive pressure can be raised
which forces the sap back to the surface of the cut end. This positive pressure
equals in absolute terms the tension that existed in the sap before the plant
material was severed. If the osmotic potential of the sap can be ignored, this tension
approximately equals the total water potential.
Measurements of water potentials of these three compartments have substantiated
the cohesion-tension theory as under well watered conditions, water potentials
Chapter 1
28
decline from soil to leaves during transpiration, forming a clear gradient to induce
xylem sap flow.
1.4.2 Stem diameter fluctuations
The exchange of water between the internal storage pools and the transpiration
stream causes small but detectable changes in the stem diameter of the tree,
causing a typical day-night pattern (see Section 1.3.1). Moreover, irreversible growth
causes a more linear expansion of the stem diameter over time during well watered
conditions (Figure 1.11).
Stem growth rate of trees has been measured since the beginning of the eighteenth
century. To this end, several different devices where developed, of which the manual
band dendrometer was the most commonly applied (Studhalter et al., 1963). While
these manual ‘dendrobands’ only allow to determine average growth rates, modern
automatic dendrobands or point dendrometers enable continuous measurements at
high time resolutions.
Point dendrometers or Linear Variable Displacement Transducers (LVDTs) are based
on the displacement of a cylindrical ferromagnetic core in a hollow metallic cylinder
in which several coils are assembled (Figure 1.10 a). Shrinking or swelling of the
stem moves the core inside the coil assembly which induces a voltage output. This
output can then be related to the displacement by calibrating the point dendrometer
in a fixed set-up during which a stepwise displacement is enforced on the sensor.
Point dendrometers have the advantage that they can measure azimuthal
differences in growth rate, allowing to study the phenomenon of ‘patchy growth’,
known to occur in some species (Schmitz et al., 2008). Automated band
dendrometers, on the other hand, are assumed to provide more accurate
estimations of average radial increments as the measurements represent a mean of
all azimuthal radii (Pesonen et al., 2004). These dendrobands consist of a stainless-
steel band encircling the tree which is attached with a fastening mechanism to a
rotating potentiometer (Figure 1.10 b). A constant force in the fastening mechanism
ensures that the band rotates the axis of the potentiometer without sliding. Hence,
movements in the steel band, because of shrinking or swelling, are transmitted to
the potentiometer, creating a voltage signal. Based on a similar calibration as for the
point dendrometer, the diameter variation can then be determined.
Water transport in trees
29
v
Tree Tree
Spring-extend
sensor head
Housing
with coil
assembly
Bend relief
spring
Cable
Holder
Holder screws
Potentiometer
Stainless-steel
band
(a) (b)
Next to the above mentioned contact methods, also optical methods have been
developed to obtain measurements remotely. These are, however, much more
expensive and their use has mainly been restricted to experimental studies in
laboratory conditions (Pesonen et al., 2004). Therefore, these will not be discussed
in this work.
Figure 1.10 (a) Point dendrometer, consisting of a movable rod fixed to a spring-extend sensor
head. Shrinking and swelling of the tree causes the rod to be displaced in the housing, creating
a voltage output linearly proportional to the displacement; and (b) band dendrometer,
consisting of a stainless-steel metallic band tightened to the tree and fixed onto a
potentiometer. Stem diameter variations cause the potentiometer to turn, inducing a voltage
output again linearly proportional to the displacement.
Chapter 1
30
X Data
Sa
p f
low
SF
/ T
ran
sp
ira
tio
n T
(g c
m-2
h-1
)
0
10
20
30
40
50
60
Re
lativ
e d
iam
ete
r va
riatio
n D
(µm
)
0
10
20
30
40
50
60
70
Time (h)
0 12 24 36 48 60 72
Wa
ter
po
ten
tia
l (
MP
a)
-4
-3
-2
-1
0
(a)
(b)
SFTD
ΨstemΨsoil
Ψl
Stem diameter variations and water potentials give a qualitative measure of water
storage and flow direction and are an indication for drought stress in plants. Sap
flow measurements, however, allow a quantitative assessment of water use in trees,
besides a more profound investigation of flow directions and spatial flow variability.
While for the estimation of stem diameter variations and water potentials the
Figure 1.11 A theoretical example of measured water use variables for a well watered tree:
(a) a time lag exists between the transpiration T and the measured sap flow SF. During the
morning, the water demand at leaf level exceeds the xylem supply, causing the stem to shrink.
In the afternoon, the stomata start to close, reducing transpiration while sap is still being
transported upwards, causing the stem to swell. Overall, a net growth occurs as new cells are
formed; and (b) the stem (Ψstem), leaf (Ψl) and soil (Ψsoil) water potential, showing a clear
gradient in which the water potential becomes more negative along the upwards flow path in
the tree.
Water transport in trees
31
measurement methods seem adequately developed, sap flow methods, although
proven indispensable in plant-water research, still hold some limitations. The
remainder of this PhD study will focus on these limitations and how to overcome
them. However, to this end, a basic notion of existing sap flow methods is
necessary. The following chapter therefore describes the most widely applied sap
flow methods, their applicability and the factors most influencing their accuracy.
33
2 2 Commonly applied sap flow
measurement methods and their
limitations
After: Vandegehuchte, M.W. & Steppe, K. (2012). Sap flux density
measurement methods: working principles and applicability. Functional Plant
Biology, 40: 213-223.
Abstract
Sap flow measurements have become increasingly important in plant science. Since
the early experiments with dyes, many methods have been developed. Most of these
are based on the application of heat in the sapwood which is then transported by
the moving sap. By measuring changes in the temperature field around the heater,
sap flow can be derived. Although these methods have the same basis, their working
principles largely vary. A first distinction can be made between those measuring the
sap flow rate (m3 s-1) such as the Stem Heat Balance and Trunk sector Heat Balance
Chapter 2
34
method and those measuring sap flux density (m3 m-2 s-1). Within the latter, the
Thermal Dissipation and Heat Field Deformation methods are based on continuous
heating, while the Heat Pulse Velocity, Tmax, Heat Ratio and Calibrated Average
Gradient methods are based on the application of heat pulses. Each of these
methods has its advantages and limitations. This chapter reviews the existing
methods to understand the basics of sap flow methodology and as a stepping stone
to allow further improvement in sap flux density measurement techniques.
2.1 Introduction
As mentioned in the general introduction of this PhD study, the scientific interest in
measuring sap flow to study plant water relations is not new. Application of dyes to
trace sap flow in stems and roots has been practiced since the beginning of the
previous century (Dixon, 1914; James & Baker, 1933; Kramer, 1940). However, as
this method necessitates plant cutting to determine the ascent of the dye,
alternatives were sought. Huber (1932) was one of the first to report the use of heat
as a tracer to determine sap flow. By measuring the time it took for a heat pulse to
reach a certain distance downstream from the heater, a measure for sap flux density
was obtained. This method was further developed by Dixon (1936) and Huber and
Schmidt (1937), adding a correction to account for conduction velocity. It was,
however, Marshall (1958) who described the analytical background of heat
conduction-convection which led to the theoretical basis for further development of
the heat pulse based sap flux density methods.
Besides these heat pulse methods, others which apply continuous heating were
developed. The work of Vieweg and Ziegler (1960) underlay the development of the
Heat Balance methods to determine sap flow rate (Daum, 1967; Cermak et al., 1973;
Kucera et al., 1977; Sakuratani, 1981, 1984; Baker & Van Bavel, 1987; Steinberg et al.,
1989) and the continuous heat sap flux density methods (Ittner, 1968; Balek &
Pavlik, 1977; Granier, 1985; Nadezhdina et al., 1998; Nadezhdina et al., 2012).
Within the existing sap flow methods, a distinction must be made between those
measuring sap flow rate (m3 s-1 or g h-1), determining the total sap flow in a plant
stem or stem section, and those measuring sap flux density (m3 m-2 s-1 or cm3 cm-2 h-
1), assessing the amount of sap flowing through a certain surface per time. While the
former are very useful for estimating whole plant water use, they are less suited to
Sap flux density methods and their limitations
35
investigation of variation in sap flow within the plant, e.g. radial sap flow profiles or
hydraulic redistribution. As sap flux density methods can discern spatial differences
in sap flux density within the plant, whether circumferentially, radially or vertically,
they allow more detailed investigation of hydraulic plant traits. Assessment of radial
variation can be obtained by applying multiple sensors or incorporating
measurement points at different depths within a single sensor.
Sap flow rate can be measured by either the Stem Heat Balance (SHB) or Trunk Heat
Balance (THB) method. Both methods solve the heat balance over a stem section of
the plant during continuous application of heat to the tissue, applying a constant or
variable power. As these methods have been clearly described by Smith and Allen
(1996) and the operational principles of the methods remain unaltered, readers are
referred to this work for more in-depth information on sap flow rate methodology.
The purpose of this chapter is to present an updated review on recent developments
in sap flux density measurement methods as these will be the further focus of this
PhD study. By describing the underlying theory of each method and discussing
some of their most common practical and theoretical issues, we hope to encourage
further improvements. This chapter does not provide a complete description of all
sap flux density methods, readers are instead referred to the original methodology
papers for each method in the corresponding section. Neither does it provide a
description of the benefits that sap flow methods have provided in plant science nor
of sampling or scaling problems. Table 2.1 provides a comparison of the main
features of all the sap flux density methods included in this chapter.
36
Method Measures Frequency Range Zero flow
needed
NTG Wounding Wound
correction
Comments
Empirical continuous methods
Thermal
Dissipation
sap flux
density
(m3 m-2 s-1)
continuous low, moderate and high
flows
yes yes yes not developed needs empirical
calibration
Heat Field
Deformation
sap flux
density
(m3 m-2 s-1)
continuous reverse to high flows no ? yes not developed needs empirical
calibration
Theoretical heat pulse methods
Compensation
Heat Pulse
sap flux
density
(m3 m-2 s-1)
pulsed moderate and high flows no no yes Vh_corr
=a+bVh+cV
h
2
Tmax sap flux
density
(m3 m-2 s-1)
pulsed moderate and high flows depending on
diffusivitydete
rmination
no yes Vh_corr
=a+bVh+cV
h
2 needs
diffusivity
determination
Table 2.1 An overview of most common sap flux density methods, indicating the measurement frequency, in which range they
are applicable, if they are influenced by Natural Temperature Gradients (NTG) or wounding, whether wound corrections are
available and if so, which type and some important comments.
37
Heat Ratio sap flux
density
(m3 m-2 s-1)
pulsed reverse, to moderate
flows
depending on
diffusivity
determination
no yes Vh_corr
=dVh needs
diffusivity
determination
Calibrated
Average
Gradient
sap flux
density
(m3 m-2 s-1)
pulsed zero to high flows no yes yes not developed needs empirical
calibration
Chapter 2
38
2.2 Continuous heat sap flux density methods
2.2.1 Thermal dissipation (TD) method
The Thermal Dissipation method (TD), often referred to as TDP (thermal dissipation
probe) or HD (heat dissipation) method, as developed by Granier (1985, 1987) based
on the work of Vieweg and Ziegler (1960), is the most widely applied sap flux
density method because of its simplicity and low costs. It enables low, average and
high sap flux density estimations but needs zero flow conditions for its calculations.
The method relates sap flux density SFD (m3 m-2 s-1) to a temperature difference ∆T
(K), measured between a constant heated probe and an unheated probe located 10
cm lower in the xylem, based on an experimental regression for three species
(Pseutotsuga menziessii (Mirb.) Franco, Pinus nigra Arnold and Quercus pedunculata
Ahrh.) and artificial columns filled with synthetic fibre and sawdust:
1.231
00.000119
T TSFD
T (2.1)
where ∆T0 is the temperature difference ∆T assessed during a period of zero flow.
The method is not capable of distinguishing flow direction as reverse flow will also
decrease ∆T. Moreover, the original assumption of Granier (1985) that the
experimental regression coefficients as shown in Eq. 2.1 are species independent,
which was confirmed for Prunus malus and Castanea sativa (Köstner et al., 1998),
has been contested by many studies. Underestimations, ranging between 6 and 90 %,
have been reported for a wide variety of species when comparing the TD to other
methods (Lundblad et al., 2001; Bovard et al., 2005; Silva et al., 2008; Iida & Tanaka,
2010) or during new calibration experiments on excised stem or branch segments
(de Oliveira Reis et al., 2006; Taneda & Sperry, 2008; Bush et al., 2010; Hultine et al.,
2010; Steppe et al., 2010), cut trees (Lu & Chacko, 1998; Uddling et al., 2009) or
potted plants (Braun & Schmid, 1999; McCulloh et al., 2007). Several possible
reasons have been indicated for these underestimations (Lu et al., 2004), including
deviations from the original sensor design, gradients in the radial SFD profile
(Clearwater et al., 1999; Wullschleger et al., 2011) and wound effects (Wullschleger
et al., 2011). Moreover, Clearwater et al. (1999) have shown that if the probe is partly
installed in non-conductive tissue, large underestimations occur. Therefore, they
suggested the following correction:
Sap flux density methods and their limitations
39
msw
T b TT
a
(2.2)
with ∆Tsw
being the corrected temperature difference for the portion of the heated
probe within conductive sapwood, ∆Tm the temperature difference for the portion of
the probe in inactive xylem (assumed equal to ∆T0) and a and b the proportion of
the length of the heated probe in contact with the sapwood and inactive xylem,
respectively. This correction, however, necessitates an accurate estimation of the
position of boundaries between active and inactive xylem that are spanned by the
probe, which is often difficult to obtain in practice without destructive
measurements.
Hence, while the original goal of the TD method was to formulate a generally
applicable, species independent empirical relation between the measured
temperature ratio and sap flux density, it is now clear that species or even tree
specific calibrations are necessary to obtain accurate results. Given these specific
calibrations, the TD method enables measurements of low, average and high SFD if
zero flow occurs to determine ∆T0. In practice, however, zero flow is often not
reached because of night-time water uptake for vegetative or reproductive growth,
replenishment of internal storage (Zweifel et al., 2001; Steppe et al., 2006), Münch
counterflow (De Schepper & Steppe, 2010) and water loss due to a high vapour
pressure deficit in combination with a high wind speed (Snyder et al., 2003). In these
cases, ∆T0 values will be underestimated, leading to underestimations of SFD.
Therefore, it has been suggested to use the maximum ∆T0 value reached during a
measurement campaign if destructive determination of ∆T0 by cutting the sapwood
above and below the sensor is not possible (Lu et al., 2004). If, however, reverse flow
occurs, this procedure would lead to overestimations of SFD. Hence, while the TD
method allows many repetitions given its low costs and is easy to apply, which
explains its popularity in ecophysiological research, it is mainly suited to determine
relative flow changes as accurate sap flux density measurements require specific
calibrations and a correct estimation of zero flow.
2.2.2 Heat field deformation (HFD) method
Like the TD method, the HFD method is based on temperature changes measured in
a changing heat field around a continuously heated needle. However, while the TD
method only measures axial temperature differences, the HFD method also consists
Chapter 2
40
of a tangential needle, making it sensitive towards a wide range of sap flux densities
(Nadezhdina et al., 1998; Nadezhdina et al., 2012). Moreover, thanks to the
symmetrical axial needle configuration, also zero and reverse flows can be
determined (Figure 2.1). The first needle is installed above the heater (axial
direction), the second needle next to the heater (tangential direction) and the third
needle below the heater (axial direction). Temperature differences measured
between the upper and lower (axial) needles (∆Tsym
) allow for both bi-directional and
very low flow measurements. The temperature differences measured between the
tangential and the lower axial needle (∆Tas) are important to distinguish high from
low sap flux densities. Additionally, the HFD sensor needles are equipped with
thermocouples at several depths, enabling radial sap flux density profile
assessment. This feature can, however, also be incorporated in the other sap flux
density methods.
(a) (b)
Figure 2.1 (a) Schematic of a tangential section of the stem xylem with arrangements of the
thermocouples around the heater of the HFD sensor; and (b) Schematic of the HFD sensor
installed in the sapwood (SW) of a stem. Two temperature differences are measured: the
symmetrical temperature difference (dTsym
) and the asymmetrical temperature difference
(dTas). The third temperature difference (dT
s-a) can be calculated as the difference between
dTsym
and dTas. After Nadezhdina et al. (2012).
Sap flux density methods and their limitations
41
Basically, the HFD method is founded on an empirical temperature ratio which has
shown to be related to sap flux density (Nadezhdina, 1988; Nadezhdina et al., 1998;
Nadezhdina, 1999; Nadezhdina et al., 2012)
0( ) 1
s a s a ax
as tg sw
T T ZSFD D
T Z L (2.3)
with ∆Ts-a
the temperature difference between the axial downstream and tangential
measurement needle, ∆T0(s-a)
this difference at zero flow (originally referred to as the
K value (Nadezhdina et al., 1998)) and ∆Tas the temperature difference between the
tangential and axial upstream needle, respectively. This temperature ratio is linked
to SFD by multiplication with thermal diffusivity D (m2 s-1), a spatial correction
factor Zax Z
tg
-1 and a correction for sapwood depth Lsw
(m). For D, a nominal value of
2.5×10-3 cm² s-1 is typically used as suggested by Marshall (1958). The addition of these
terms to the original HFD temperature ratio are, however, somewhat random as they
are empirically derived and therefore do not seem based on found thermodynamics
(Nadezhdina et al., 2012).
Unlike the TD method or heat balance sensors, zero flow is not necessary to
determine ∆T0(s-a)
as it can be derived by linear extrapolation of ∆Tas or ∆T
s-a vs
∆Tsym
/∆Tas with ∆T
sym the temperature difference between the axial downstream and
upstream needle (Figure 2.2). Because of its sensitivity towards a wide range of sap
flux densities and the integration of measurements at multiple depths, the HFD
method has played a crucial role in the research on hydraulic redistribution and
radial sap flux density profiles (Nadezhdina et al., 2002; Nadezhdina et al., 2009;
Nadezhdina, 2010; Nadezhdina et al., 2010; Leonardo Reyes-Acosta & Lubczynski,
2012).
Chapter 2
42
(a) (b)
(c) (d)
ΔT0(s-a)
ΔT0(s-a) ΔT0(s-a)
ΔT0(s-a)
ΔT0(s-a)
ΔT0(s-a)
2.2.3 Natural temperature gradients
Natural temperature gradients (NTG) are temperature gradients occurring in the
sapwood of plants that are not caused by the intentional heating from the sap flow
measuring methods. These gradients have, amongst others, been attributed to
differences in thermal heat storage in the soil, stem and root tissues resulting in
temperature differences between the sap and the plant tissues (Cermak & Kucera,
1981; Köstner et al., 1998; Do & Rocheteau, 2002a) and to the influence of direct
solar radiation (Lu et al., 2004). While these influences can be minimized by
Figure 2.2 (a) HFD temperature ratio with a schematic diagram of the gradually cutting of
shoots of a branch to provide conditions of zero flow; (b) dTas and dT
s-a for measurements when
the branch is still intact (no cutting); (c) dTas and dT
s-a for measurements when the branch is
cut at position 1; and (d): dTas and dT
s-a for measurements when the branch is cut at position 2.
After Nadezhdina et al. (2012).
Sap flux density methods and their limitations
43
shielding the gauge from radiation and locating it sufficiently high above the
ground, the effect of natural gradients can never be excluded completely.
The influence of NTG on the TD method has been extensively studied and has
shown to lead to errors of over 100% if not corrected for (Goulden & Field, 1994; Do
& Rocheteau, 2002a, 2002b; Lu et al., 2004; Reyes-Acosta et al., 2012). The first
attempts to correct for NTG were focussed on measuring NTG on neighbouring trees
or on different positions in the tree that are being monitored (Köstner et al., 1998).
These methods, however, require NTG to be uniform within or between trees.
Therefore, more recent corrections are based on NTG measurements by periodically
switching the heater off. Do & Rocheteau (2002b) developed a cyclic TD system for
which a specific calibration was developed to account for non-steady state
temperatures regimes, significantly reducing the influence of NTG. This method was
updated by Ayutthaya et al. (2010) who improved the calibration coefficients.
Recently, Reyes-Acosta et al. (2012) further improved this method by extrapolating
the TD signal to thermal equilibrium, allowing the use of the original Granier
calibration. Moreover, their method enabled shorter measuring intervals, leading to
a higher measurement resolution. A further improvement of this method would be
the use of a single heated probe as was applied by Do et al. (2011) for their original
cycling method as this would reduce costs and complexity.
The influence of NTG on HFD measurements has not been reported yet. Because of
the shorter distances between the needles and their closer proximity to the heater,
the influence of NTG is expected to be smaller for the HFD than for the TD method.
2.3 Heat pulse sap flux density methods
Unlike the continuous heat methods mentioned above, heat pulse methods are
based on the fundamental heat conduction-convection equation as presented by
Marshall (1958), derived from Carslaw and Jaeger (1947), for an instantaneous ideal
heater. All heat pulse methods derive heat pulse velocity Vh from measured
temperature differences at specific locations around the heater after application of
a heat pulse. As the measurement procedures are based on the dissipation of the
heat after application of the pulse, heat pulse methods cannot measure
continuously, with the measurement frequency depending on the time span needed
Chapter 2
44
to reach thermal equilibrium again after having applied the heat pulse. These heat
velocities then need to be converted to sap flux densities:
( )d dwh
s s
cSFD MC V
c
(2.4)
where SFD is the sap flux density (m3 m-2 s-1), Vh the heat velocity (m s-1), MC the
sapwood water content (weight of water over dry weight of wood), cdw
the specific
heat capacity of the woody matrix (1200 J kg-1 K-1, Edwards and Warwick (1984)), ρd
the dry density of the sapwood (kg m-3), ρs the density of the sap (assumed to be the
density of water, 1000 kg m-3) and cs the specific heat capacity of the sap (assumed
to be that of water, 4186 J kg-1 K-1, Edwards and Warwick (1984)). Dry wood density
and water content are usually derived from wood-core measurements, implying that
variations in MC are often not taken into account, unless other techniques are
applied such as Time Domain Reflectometry (Wullschleger et al., 1996a; Nadler et
al., 2003; Nadler et al., 2006), Frequency Domain Reflectometry (Hao et al., 2013),
Magnetic Resonance Imaging (Van As et al., 2009) or vibration methods (Iki et al.,
2009). However, these methods require additional equipment and analysis and the
gravimetric method remains the reference method to determine MC in trees.
As heat pulse methods are based on temporal temperature differences at the same
measurement position, unlike continuous methods which apply spatial temperature
differences between different positions, they are hardly susceptible to NTG (with the
exception of the Calibrated Average Gradient method) (Table 2.1).
2.3.1 Compensation Heat Pulse velocity (CHP) method
The CHP method, often also referred to as heat pulse velocity (HPV) method, is
based on the time tc after application of the heat pulse at which the temperature at a
distance xup
upstream of the heater needle is equal to the temperature at a distance
xdown
downstream of the heater (Swanson, 1972; Swanson & Whitfield, 1981):
2
down up
h
c
x xV
t
(2.5)
This method has the advantage that it is independent of thermal diffusivity, a
sapwood characteristic that has to be determined for the Tmax and HR method.
However, Eq. 2.5 is developed for an ideal heat pulse with an infinitesimally small
Sap flux density methods and their limitations
45
length and is not theoretically correct for a step heat pulse, leading to
underestimations that increase with pulse length.
Moreover, CHP fails to measure reverse, low or very high flows (<5 cm h-1 and >100
cm h-1) as then no intersection between the upstream and downstream temperatures
occur. Besides, Green et al. (2009) have shown that for low wood water contents
(from 28 to 55%), Vh decreases for increasing water contents. Despite these
shortcomings, the CHP method is widely applied for irrigation purposes (e.g.
Edwards & Warwick, 1984; Green & Clothier, 1988; Tognetti et al., 2004; Pereira et
al., 2007; Madurapperuma et al., 2009a; Madurapperuma et al., 2009b) and to assess
water use of trees in ecophysiological research (e.g. Morris & Collopy, 1999; Hirose
et al., 2005; Liu et al., 2012; Ma et al., 2012).
2.3.2 Tmax method
The Tmax method (Cohen et al., 1981), determines Vh based on the time t
m at which
the temperature measured at a distance d from the heater becomes maximal:
2 4
m
h
m
d D tV
t (2.6)
with D the thermal diffusivity of the sapwood (m2 s-1), determined during zero flow
conditions:
2
4
m
dD
t (2.7)
Eq. 2.6 and 2.7 were later updated by Kluitenberg & Ham (2004) for step heat pulses
instead of instantaneous heat pulses:
2
0
0 0
4ln 1
( )
h
m m m
tD dV
t t t t t (2.8)
12
0
0 0
ln4 ( )
m
m m m
t tdD
t t t t t (2.9)
where t0 is the heat pulse duration.
Green et al. (2003) have shown that a curve smoothing procedure led to better
results as tm is difficult to accurately determine from the raw temperature data
Chapter 2
46
during low flows because of noise. However, even with curve smoothing procedures,
the Tmax method cannot distinguish between zero and low flux densities (<20
cm3 cm-2 h-1) as the relationship between tm and SFD is non-unique at these low flux
densities (Figure 2.3) (Becker, 1998). Besides, as for the heat balance and the TD
method, zero flow conditions are difficult to ensure, making non-destructive D
estimations impractical. Both Cohen et al. (1981) and Green et al. (2003) have,
however, confirmed that a 10% error in D only leads to errors of up to 3% in Vh and
hence SFD. Because its the higher complexity in comparison to the CHP method, the
Tmax method has been less frequently applied. Nevertheless, the field of plant-
water research has undoubtedly benefited from its use (e.g. Cohen, 1991; Schiller &
Cohen, 1998; Cohen et al., 2008).
Vh (cm h
-1)
0 20 40 60 80 100 120 140 160
t m (
s)
30
40
50
60
70
80
90
100
110
2.3.3 Heat Ratio (HR) method
In an answer to the difficulties in measuring low flows with the CHP and Tmax
method, Burgess et al. (2001a) developed the HR method, based on a suggestion
presented in Marshall (1958):
Figure 2.3 Time to maximum (tm) versus heat velocity V
h based on the FEM output for a
measurement probe at 1 cm downstream from the heater, a water content of 0.75, a dry wood
density of 550 kg m-3 and an axial and tangential thermal conductivity of 0.63 and 0.42
W m-1 K-1, respectively. Wound effects were included in the model.
Sap flux density methods and their limitations
47
ln
downh
up
TDV
x T (2.10)
with ∆Tdown
and ∆Tup
the increases in temperature at equal distances x (m)
downstream and upstream from the heater needle, respectively. In practice the
temperature ratio ∆Tdown/
∆Tup
does not remain constant with time because of non-
ideality due to wound effects. However, the rate of change in this temperature ratio
becomes negligible after about 60 s. Therefore, the average temperature ratio of
measurements between 60 and 100 s after application of the heat pulse are used to
determine Vh.
As for the Tmax method, D needs to be determined. Burgess et al. (2001a) based this
determination on previous work of Swanson (1983) who applied an empirical
equation deducted by Siau (1971), only necessitating a wood core sample to
determine MC and ρd. Another option is to determine D according to Eq. 2.7. For the
HR method, however, a 10% error in D will lead to an equal error in Vh, making this
option less favorable as zero flow can be difficult to ensure.
Given a good estimation of D, the HR method has proven its value for measuring low
and reverse flows. It is, however, limited for high flows (>55 cm3 cm-2 h-1) (Bleby et
al., 2008) as for these flows, the ∆Tup
signal decreases, reducing the sensitivity of Eq.
2.10. Nevertheless, since its description by Burgess et al. (2001a), the HR method
has rapidly gained popularity and has been applied throughout the entire spectrum
of plant-water research, ranging from irrigation (Madurapperuma et al., 2009a) and
the impact of tree and stand structure on tree water use (Ambrose et al., 2009;
Pfautsch et al., 2010) to those phenomena requiring accurate measurements of low
and reverse flow such as nocturnal sap flow (e.g. Dawson et al., 2007; Fisher et al.,
2007) and hydraulic redistribution (e.g. Hultine et al., 2003b; Burgess & Dawson,
2004; Oliveira et al., 2005a; Oliveira et al., 2005b; Scott et al., 2008).
Recently, Clearwater et al. (2009) developed an external HR method enabling sap
flux density measurements for small diameter stem (< 5 mm). D was derived based
on Eq. 2.7 and was found to be dependent on both the stem and the cork material
applied to fix the sensor. Promising results were obtained for low and reverse flows
(-7.5 cm h-1<Vh<7.5 cm h-1).
Chapter 2
48
2.3.4 Calibrated Average Gradient (CAG) method
Another promising heat pulse method, the CAG method, has been proposed by Testi
& Villalobos (2009). These authors extended the CHP method to enable low and even
zero flow measurements. Both results from Finite Element Models (FEM) and field
experiments confirmed that for low flows (Vh<30 cm h-1), V
h was linearly correlated
to ∆Ta, the average temperature difference between the downstream and upstream
temperature sensors during the 180 seconds after application of the heat pulse
(Figure 2.4). By extrapolating this linear relationship, which is only dependent on
sensor characteristics and thermal properties of the sapwood, low and zero flows
can be measured based on ∆Ta, while for high flows, the original CHP method is
applied. The use of the average temperature gradient, however, implies that the CAG
method is likely to be influenced by NTG. While for the other methods, only the
temperatures before and after application of the heat pulse are of importance, here
the temperature difference between downstream and upstream positions is needed
during the entire 180 s. By extrapolating this linear relationship, which is only
dependent on sensor characteristics and thermal properties of the sapwood, low
and zero flows can be measured based on ∆Ta, while for high flows, the original CHP
method is applied.
The use of the average temperature gradient, however, implies that the CAG method
is likely to be influences by NTG. While for the other methods, only the
temperatures before and after application of the heat pulse are of importance, here
the temperature difference between downstream and upstream positions is needed
during the entire 180 s. Hence, while for the other methods the relative temperature
changes are not influenced by a shift in absolute temperature, this will likely affect
the CAG method, reducing the ∆Ta signal for positive gradients from roots to crown
and vice versa and, hence, influencing the linear relationship between Vh and ∆T
a.
Therefore, the effects of NTG on the CAG method should be further investigated.
Moreover, if the thermal properties of the sapwood change significantly during the
measurement period, a new linear relationship should be established.
Sap flux density methods and their limitations
49
2.4 Sensor spacing
All sap flux density methods are based on the insertion of measurement and heater
needles into the sapwood. With exception of the TD method, all methods have probe
spacing directly incorporated in their sap flux density equations. Hence, while for
the TD method exact spacing is less important as long as the reference probe is not
influenced by the heated probe, for the other methods correct spacing is crucial
(Cohen et al., 1981; Swanson, 1983; Burgess et al., 2001a). Probe misplacement can
be assessed by placing over-length probes in the drill holes, enabling measurement
of the spacing and angle between the probes (Hatton et al., 1995). Moreover, for the
HR method, Burgess et al. (2001a) measured probe placement in situ, based on zero
flow conditions. However, parallel placement of the needles remains crucial for
accurate results and is often difficult to ensure, especially at large sapwood depths.
If probes are installed parallel, but needles are tangentially displaced, this cannot be
taken into account. Generally, applying a specific drill-bit template for each heat
pulse method can improve probe positioning during sensor installation.
Figure 2.4 Vh versus ∆T
a for Olea europaea. The line is the regression of V
h on ∆T
a obtained
with the data pairs where ∆Ta<0 K, taken during 24 h (adapted from Testi and Villalobos
(2009)).
Chapter 2
50
2.5 Wounding
When inserting probes in the sapwood, flow is locally obstructed with the
obstructed zone dependent on sensor geometry and probe size and, to a lesser
extent, probe material (Swanson & Whitfield, 1981; Barrett et al., 1995; Green et al.,
2003). Barrett et al. (1995) have shown that wounding also affects wood density and
fibre direction, especially in the axial direction. Besides these direct wound effects,
probe insertion also induces the formation of wound tissue which alters wood
properties and, hence, heat dissipation in this wood in the longer term (Moore et al.,
2009). This long-term effect can be avoided by regularly reinstalling sensors during
long-term experiments, although little research has been done on the required
frequency of reinstallation (Moore et al., 2009).
Short-term wounding, on the other hand, has been assessed to be an important
error-inducing factor for the TD method (Wullschleger et al., 2011). These authors
developed a numerical heat flow model to assess TD performance, allowing
investigation of error inducing factors both separately and combined. They
determined that physical disruption of the xylem due to wounding was a significant
cause of error, besides gradients in the radial sap flux density profile.
Moreover, Wullschleger et al. (2011) have shown that the TD method is sensitive to
changes in thermal conductivity and, hence, is dependent on sapwood
characteristics. This implies that for a specific tree species, the calibration could
change due to varying dry wood density of the sapwood and, even for a single tree,
could change due to variations in sapwood water content as wounding progresses.
According to their modelling results, a combination of these error inducing factors
can lead to both under- and overestimations of sap flux density when using the
original calibration coefficients. These authors justly warn users of the TD method
to interpret their results with caution and plead for an approach where numerical
modelling is combined with updated calibration coefficients to improve TD method
accuracy. Unlike for the TD method, wounding has not been thoroughly assessed for
the HFD method, although it is expected to have a similar influence on the results.
Next to the continuous heat methods, flow path obstruction due to wounding also
greatly influences the sap flux density results for heat pulse methods. Based on
Finite Element Modelling (FEM), it has been shown that wounding partially interrupts
Sap flux density methods and their limitations
51
sap flow, leading to underestimations of Vh and hence SFD of up to 50% and more
(Swanson, 1983; Burgess et al., 2001a; Green et al., 2003). Therefore, wound
correction equations were developed for the existing heat pulse systems based on
FEM. Wound width has been shown to have a much larger effect than probe
material, calibration factors based only on wound width therefore seem sufficient
for a given sensor configuration (Swanson, 1983; Green et al., 2003). For the CHP
method, Swanson & Whitfield (1981) developed readily applicable wound correction
coefficients a, b and c for the correction equation Vh_corr
=a+bVh+cV
h
2, where Vh_corr
is
the heat velocity corrected for wound effects (Table 2.1). While Cohen et al. (1981)
derived correction factors for the Tmax method empirically, Green et al. (2003)
presented similar wound corrections for the Tmax method as those developed by
Swanson and Whitfield (1981) for the CHP method. For the HR method, Burgess et
al. (2001a) have shown that a linear correction equation is sufficient.
For hardwood species with a markedly non-uniform distribution of sap-conducting
vessels, however, an additional correction factor besides the wound correction may
be necessary. This type of wood diverges more from the assumption of thermal
homogeneity, on which the heat conduction-convection equations are based, than
for softwoods or hardwoods with closely-spaced and more uniform xylem elements
(Swanson, 1983; Green & Clothier, 1988). This correction factor can be empirically
determined or derived from enhanced FEM including vessel anatomy.
In the various models used to assess wounding, flow obstruction is implemented as
a region of zero flow starting from the most upstream sensor needle and stretching
on downstream with a width slightly larger than the sensor needles. While the effect
of different wound widths and sapwood water contents have been simulated, the
axial length of the zero flow region has never been mentioned (Swanson & Whitfield,
1981; Burgess et al., 2001a; Green et al., 2003). Nevertheless, it is likely that this
length will differ depending on wood anatomy. In addition, apart from flow
obstruction, wood properties also can be locally altered due to installation. It would
be interesting to investigate wound effects for different sapwood types and assess
possible differences in wound correction factors. Also, FEM could be improved by
including differences in vessel anatomy. In this way, the accuracy of heat pulse
based sap flux density estimates might be enhanced.
Chapter 2
52
2.6 General conclusions
Throughout the years, many sap flow methods have been developed, each with their
advantages and disadvantages. Heat balance methods integrate flow in the entire
stem or in a large stem section of the plant, giving a good indication of total plant
water use. Sap flux density methods, on the other hand, give more precise
information on flow directions and spatial flow distribution. For many methods,
wounding influences sap flow results. Despite the existing wound corrections for
the heat pulse methods, a more thorough insight in wound effects, including long-
term experiments combining sap flow methods with FEM and more advanced
techniques such as Magnetic Resonance Imaging, will likely further improve sap
flow methodology.
So far, the HFD is the only method enabling measurements across the entire
naturally occurring sap flow range. However, the link between SFD and the HFD
temperature ratio is somewhat obscure, raising questions on the accuracy of HFD
measurements. Therefore, the next chapter discusses the original HFD equation (Eq.
2.3) more thoroughly.
53
3 3 Erroneous use of thermal
diffusivity in the Heat Field
Deformation method
After: Vandegehuchte, M.W. & Steppe, K. (2012). Interpreting the Heat
Field Deformation method: Erroneous use of thermal diffusivity and improved
correlation between temperature ratio and sap flux density. Agricultural and
Forest Meteorology, 162-163: 91-97.
Abstract
The Heat Field Deformation (HFD) method is a modern technique to assess sap flux
density in trees by applying an equation which relates an empirical temperature
ratio to the thermal diffusivity of the sapwood. However, this relation is based on a
misinterpretation of thermal diffusivity, leading to physically incorrect units of sap
Chapter 3
54
flux density. Moreover, the HFD method has recently been shown to occasionally
underestimate actual sap flux densities, raising the question whether species
specific calibration is necessary. This chapter calls attention to a correct
interpretation of thermal diffusivity and investigates the correlation between sap
flux density and the HFD temperature ratio based on a 3D Finite Element Model. It is
shown that the original terms linking the HFD temperature ratio to sap flux density
do not follow fundamental thermodynamics and, therefore, the HFD method should
be considered merely empirical. Besides, the method is not only dependent on
sapwood characteristics but also on sap flux density itself, necessitating a specific
calibration equation.
3.1 Introduction
The main goals of the development of the Heat Field Deformation (HFD) method
were (i) establishing a good linear correlation between measured temperature
signals and sap flow for both low and high sap flow rates, (ii) the possibility to
measure reverse flows and (iii) the ability to perform sap flow calculations without
the need to assume night-time zero flow conditions. Moreover, it was also an
objective to be able to determine sap flux densities at different depths within the
sapwood (Nadezhdina et al., 1998; Nadezhdina et al., 2012).
As explained in section 2.2.2, the HFD method is principally based on the dynamics
of a temperature ratio including a symmetrical (axial) and an asymmetrical
(tangential) temperature difference to characterize the changing heat field around a
continuous heater for different sap flux densities (Figure 2.1). To relate this
temperature ratio to sap flux density, it was multiplied by thermal diffusivity based
on the approaches of Marshall (1958) and Saddler & Pitman (1970) to determine sap
flow by heat based sensors. To obtain units of m3 m-2 s-1, the thermal diffusivity was
then multiplied by Zax Z
tg
-1 Lsw
-1 (Eq. 2.3), with Zax the distance between the heater and
axial measurement needles, Ztg the distance between the heater and tangential
measurement needle and Lsw the sapwood depth. Here, L
sw Z
tg was considered to be a
measure for the sapwood cross-sectional area where deformation of the heat field
occurs and hence sap is flowing while the implementation of Zax Z
tg
-1 partially corrects
for needle spacing (Nadezhdina et al., 1998; Nadezhdina et al., 2012). Hence, Eq. 2.3 is
supposed to determine actual sap flux density (m3 m-2 s-1).
Accuracy and applicability of the HFD method
55
Without doubt, Eq. 2.3 has its merits in sap flow research, having revealed several
tree physiological phenomena, never measured before. It has been used to
investigate hydraulic redistribution (Nadezhdina et al., 2006; 2008; 2009; 2010),
xylem structure and functionality (Nadezhdina, 2010), radial sap flow (Nadezhdina
et al., 1998; Jimenez et al., 2000; Saveyn et al., 2008; Steppe et al., 2009) and
modelling of water use and transpiration (Chiesi et al., 2002; Oltchev et al., 2002;
Verbeeck et al., 2007; Van der Zande et al., 2009). The method appeals because of its
sensitivity across a wide range of sap flow rates and this for several sapwood
depths, even though recently deviations between actual sap flux densities
determined gravimetrically and HFD measured sap flux densities have been
reported (Steppe et al., 2010).
This chapter investigates the thermodynamic background of the HFD method and
its parameters and points out some misunderstandings concerning its units.
Moreover, by applying a FEM, the accuracy of the HFD method is questioned and a
mathematical relation between sap flux density and the HFD temperature ratio is
developed to correct its original flaws.
3.2 Thermodynamic background HFD method
When looking at the measured temperature differences (Eq. 2.3), it is clear that the
heat transport on which the HFD method is based, consists of two dimensions: the
axial and tangential dimension. This can be thermodynamically explained by the
assumption of a perfect linear heater in a homogeneous medium: by equally heating
the stem in its radial direction, the temperature field will be radially constant. This
is one of the fundamental assumptions of heat-based sap flow methods applying a
linear heater (Marshall, 1958; Burgess et al., 2001b; Tatarinov et al., 2005).
Therefore, these methods can be considered two dimensional. The radial profile
which can be obtained by the HFD method is thus the combination of several two
dimensional measurements at different depths. Therefore, the application of Lsw
as a
radial parameter in this two dimensional method is incorrect.
The main reason to include Lsw
was to obtain units of m3 m-2 s-1 (Nadezhdina et al.,
2012). However, even though multiplication of thermal diffusivity with Zax Z
tg
-1 Lsw
-1
leads to these units, they are not units of sap flux density. Thermal diffusivity D (m2
s-1), as a measure of the rate by which the sapwood can absorb heat from its
Chapter 3
56
surroundings (Bouguerra, 2001), is the ratio of the thermal conductivity K (W m-1 K-1)
of the sapwood on the one hand and the product of the fresh density ρ (kg m-3) and
the heat capacity c (J kg-1 K-1) of the sapwood on the other hand:
KD
c
(3.1)
In this formula, thermal conductivity K (W m-1 K-1) is defined as the amount of heat
flowing per time unit through a body of 1 m thickness with a surface of 1 m2 and a
temperature difference of 1 K between both surfaces:
Q dKA t T
(3.2)
with Q the amount of thermal energy (J), d the thickness of the material (m), A the
cross-sectional area of the material (m2), ∆T the temperature difference between
both surfaces (K) and t the time (s). This parameter thus describes the ability of the
sapwood to transmit heat when subjected to a temperature gradient. For axial sap
flow, A thus represents the cross-sectional area of the sapwood, while d represents
the axial dimension corresponding to the flow direction. The density of the sapwood
ρ (kg m-3) is the mass M of the volume with cross-sectional area A and thickness d.
The heat capacity c (J kg-1 K-1) is the amount of thermal energy Q’ stored in this mass
M for a temperature change ∆T of 1 K (Marshall, 1958).
To gain insight in the dimensional unit (m²) of the thermal diffusivity D, the
following equation is defined:
( )
'
Q dK d A dA t TD
Qc A tMA d M T
(3.3)
The m² thus actually represents a volume of sapwood (A d) per sapwood cross-
sectional area (A) multiplied by an axial direction d, as this is the direction of heat
flow because of sap flow (Figure 3.1). Therefore, as in Eq. 2.3 the thermal diffusivity
is multiplied by an axial and divided by a radial and tangential dimension, the units
of the original HFD equation do not represent a flux density and have no physical
meaning. To obtain the correct dimensions, it is necessary to divide by an axial
distance. Moreover, the thermal diffusivity represents the entire sapwood (both
Accuracy and applicability of the HFD method
57
wood matrix and water), leading to heat flux velocities Vh and not sap flux densities.
Hence, an additional conversion according to Eq. 2.4 would be needed to obtain SFD.
By which axial distance should the thermal diffusivity then be divided to obtain
physically correct sap flux densities? A logic choice would seem to divide by the
distance from the axial sensor needle to the heater (=Zax) as done for other heat-based
systems (Marshall, 1958; Saddler & Pitman, 1970; Cohen et al., 1981; Burgess et al.,
2001b). However, both for the systems based on Marshall (1958) and Saddler &
Pitman (1970), the sap flow equations are directly derived from the fundamental
heat conduction-convection equation. This is not the case for the HFD ratio, making
the multiplication with any parameter, even the thermal diffusivity D itself, an
arbitrary choice. Therefore, as the combination of parameters in Eq. 2.3 in relation
to the HFD ratio do not add any interpretational value to the HFD method, it should
be considered an empirical method for which any parameter linking the HFD ratio to
sap flux density, could be used, supposing a linear relation between the HFD ratio
and sap flux density. This prevents false interpretation of supposedly
thermodynamic features such as the thermal diffusivity.
Figure 3.1 Schematic representation of the HFD sensor with the dimensional units for
diffusivity and sensor spacing, with Lsw
the sapwood depth, A the sapwood cross-sectional area,
d the axial dimension corresponding to the flow direction, Zax and Ztg the axial an tangential
distance between the heater and the axial and tangential measurement needles, respectively.
Note that in this representation, no hardwood is taken into account.
Chapter 3
58
3.3 Materials and method
To thoroughly investigate the HFD method, a 3D FEM was developed. A moist wood
segment of 20 cm height and 10 cm width with a varying sapwood depth was
modelled, holding a heater needle and three measurement needles. The boundary
temperature was constant at 20 °C.
This FEM solves the partial differential equation governing heat transport in each
defined node of the 3D structure:
² ² ²
² ² ²
h h
T T T T T T Tc K cV P
t x y z x y z (3.4)
with T temperature (K), t time (s), Vh convective heat velocity (m s-1), ρ density (kg m-
3), c specific heat capacity (J kg-1 K-1) and K the vector of thermal conductivity (W m-1
K-1) of the medium (comprising of axial (Kax), tangential (K
tg) and radial (K
rad)
conductivity, respectively) in which the temperature changes take place. As moist
wood is anisotropic, containing directionally different thermal properties, Kax was
always set higher as or equal to Ktg. As the heater was inserted radially, K
rad had no
influence on the results. Ph (W m-3) is the amount of heat released in a unit of volume
at the point (x,y) per unit of time. For the measurement and heater needles, the
properties of steel were chosen for implementation in the model (ρ=7850 kg m-3,
c=475 J kg-1 K-1, K= 44.5 W m-1 K-1). Heat velocity was related to sap flux density
according to Eq. 2.4.
Simulations for a range of sap flux densities were conducted for which the ratio
(∆T0(s-a)
+∆Ts-a
) ∆Tas
-1 was calculated and compared with the sap flux density for
differences in wood properties (thermal conductivity, dry wood density and water
content) covering the natural range for woody species. To test the influence of heat
input on the HFD method, it was set between 9 and 18 W cm-1. As in the HFD
method continuous heating is applied, measurements were supposed to be stable at
120 s after the heater was switched on. The influence of the needle spacing was
tested to investigate the importance of the original correction factor Zax Z
tg
-1. For the
rest of the simulations, the same distances as mentioned by Nadezhdina et al.
(1998; 2012) were applied (Zax=15 mm, Z
tg=5 mm) as these distances were mentioned
to lead to the highest sensitivity for the HFD ratio to changes in sap flux density.
Accuracy and applicability of the HFD method
59
3.4 Results and discussion
3.4.1 Characteristics of the HFD temperature ratio
Influence of heat input
Figure 3.2a and b show the relation between the HFD ratio modelled for increasing
heat velocities (Vh) with different heat inputs. Even though for varying heat inputs
the absolute temperatures clearly differ (Figure 3.2a), the HFD ratio does not change
(Figure 3.2b). Similar results were obtained if the time to stabilization was set larger
than 120 s, confirming that the system was in thermal equilibrium after this period
of time. Therefore, for the remainder of the results, a fixed heat input q (heat input
per unit length of the heater) of 9.4 W m-1 will be used and temperature values are
always those at 120 s after its application.
Two dimensionality of the HFD ratio
Varying the sapwood depth of the 3D model while maintaining the same convective
flux did not affect the measured temperatures, confirming the theory that the HFD
method is basically two dimensional.
HFD temperature ratio q1
0 2 4 6 8 10
HF
D te
mp
era
ture
ratio
q20
2
4
6
8
10
q2=2*q1
q2=1/2*q1
q2=1.5*q1
Heat velocity Vh (cm h-1)
0 20 40 60 80 100
Te
mp
era
ture
(°C
)
20.0
20.5
21.0
21.5q 4.7 W.m
-1
q 18.8 W.m-1
Tref
Tax
Ttg
Vh
(a) (b)
Figure 3.2 (a) Tref
, Tax and T
tg at 120s after switching on the heater for different heat velocities
(and hence sap flux densities), both for a heat input of 18.8 W m-1 and 4.7 W m-1; (b) HFD
temperature ratios for increasing heat velocities (Vh) calculated with different heat inputs and
q1=9.4 W m-1.
Chapter 3
60
Linearity of the HFD ratio
The HFD method has been said to be highly sensitive towards a wide range of sap
flux densities (Nadezhdina et al., 1998; Nadezhdina et al., 2012). Figure 3.3a
confirms that the HFD ratio increases with increasing sap flux density, but not
linearly. The relative error, calculated as the difference between the sap flux density
and the HFD ratio divided by the sap flux density, decreases for increasing sap flux
densities (Figure 3.3b), even though the absolute error increases (Figure 3.3a).
Multiplication of the HFD ratio with constant parameters as is done in Eq. 2.3 can,
hence, reduce the absolute errors, but can not resolve the relative sap flux density
dependency of the ratio. As a result of these findings,the measurements at different
sapwood depths will only give an approximation of the radial profile as the relative
error will be different for each depth, given the radial variation in sap flux density.
Moreover, this relative discrepancy is not only influenced by the sap flux density but
is also depending on the axial and tangential conductivity (Figure 3.4a) and dry
wood density (Figure 3.4b), even though the effect of the latter on the HFD ratio is
rather small (a 40% difference in dry wood density only led to a maximal difference
of 12% difference in HFD ratio). The water content does not influence the ratio
significantly if all other parameters remain unchanged (Figure 3.4c). In reality,
however, changes in water content are coupled with changes in thermal
Sap flux density (cm3 cm-2 h-1)
0 20 40 60 80
HF
D r
atio
0
20
40
60
80
0 20 40 60 80
rela
tive e
rror o
f HF
D ra
tio
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00(a) (b)
Figure 3.3 (a) Relationship between the HFD ratio and the sap flux density. The dashed line
represents the 1:1 line; and (b) relative error of the HFD ratio, calculated as the difference
between the sap flux density and the HFD ratio divided by the sap flux density,
Accuracy and applicability of the HFD method
61
conductivity. Hence, variation in wood properties between tree species can lead to
large relative differences in HFD ratio for the same sap flux density (Figure 3.4d).
Besides, even variation within species, both spatially and temporally, could induce
changes in the HFD ratio, although it is expected that these differences are rather
small as the variation in thermal parameters and dry wood density within species is
much smaller than between species (Skaar, 1988).
Influence of needle spacing on the HFD ratio
Figure 3.5a shows that changes in Zax hardly influence the HFD ratio if Z
tg remains
unaltered, while changes in Ztg lead to large differences for moderate and high flows
(>20 cm3 cm-2 h-1). Apparently, the ∆T0(s-a)
value largely compensates for changes in
Zax. Moreover, if Z
ax is changed, this will only have a small effect on the T
as signal for
Sap flux density (cm3.cm-2.h-1)
0 20 40 60 80 100
HF
D r
atio
0
10
20
30
40
50
Kax 0.75; Ktg 0.65
Kax 0.85; Ktg 0.65
Kax 0.65; Ktg 0.65
Kax 0.75; Ktg 0.55
Kax 0.75; Ktg 0.45
Sap flux density (cm3.cm-2.h-1)
HF
D ra
tio
0
5
10
15
20
25
30
d400
d490
d550
d625
Sap flux density (cm3 cm-2 h-1)
0 20 40 60 80 100
HF
D r
atio
-5
0
5
10
15
20
25
30
MC 0.75
MC 0.85
MC 0.91
0 20 40 60 80 100
HF
D r
atio
0
10
20
30
40
Rela
tive d
iffere
nce
0.2
0.3
0.4
0.5
0.6
0.7
Kax 0.70; Ktg 0.65; MC 1; d 450
Kax 0.75; Ktg 0.45; MC 0.55; d 600
Relative difference
Sap flux density (cm3 cm-2 h-1)
(a) (b)
(c) (d)
Figure 3.4 Sap flux density dependency of (a) the HFD ratio for different axial (Kax) and
tangential (Ktg) thermal conductivities (W m-1 K-1), a dry wood density (ρ
d) of 490 kg m-3 and a
water content of 0.91; (b) the HFD ratio for different dry wood densities(ρd) for K
ax=0.75 W m-1
K-1, Ktg=0.65 W m-1 K-1 and MC=0.91; (c) the HFD ratio for different water contents (MC) with
Kax=0.75 W m-1 K-1, K
tg=0.65 W m-1 K-1 and ρ
d =550 kg m-3; and (d) HFD ratios for varying wood
properties and the relative difference between them.
Chapter 3
62
high flows as then the Tref
needle is less influenced by the heater. Hence, displacing
this needle will only lead to small differences in Tref
. If, however, Ztg is altered, then
for high flows the Tas signal will be much more affected as the T
as needle should be
in close proximity of the heater to ensure sufficient sensitivity towards high flows.
In Figure 3.5b, it can be seen that there is a more even spread of HFD ratios if these
are multiplied with the Zax Z
tg
-1 term. When comparing, for instance, the spacing Zax15
Ztg2.5 with Z
ax10 Z
tg5, the Z
ax Z
tg
-1 term indeed led to a smaller deviation in HFD ratios
as the difference in Figure 3.5b is smaller in comparison to the difference in Figure
3.5a even though for sap flux densities >60 cm3 cm-2 h-1 they still greatly differ.
Moreover, for other combinations (for instance Zax15 Z
tg5 and Z
ax20 Z
tg5), the
divergence even increases when the Zax Z
tg
-1 term is applied. The absolute changes in
HFD ratio with or without the term Zax Z
tg
-1 due to changes in needle spacing will be
dependent on the thermal properties of the wood (data not shown), although the
same conclusions hold. Hence, even though the term Zax Z
tg
-1 clearly influences Eq.
2.3, it cannot be considered an absolute spacing correction.
3.4.2 From temperature ratio to sap flux density
As the temperature ratio is dependent on wood properties and needle spacing, this
dependency needs to be included in the link with sap flux density. This is in
agreement with the lab and field experiments of Steppe et al. (2010), who stated that
recalibration of the HFD method might be necessary for each new tree species.
Sap flux density (cm3 cm-2 h-1)
0 20 40 60 80 100
HF
D r
atio
0
10
20
30
40
50
0 20 40 60 80 100
HF
D ra
tio x
Zax Z
tg-1
(a) (b)
Zax 15; Ztg 5
Zax 20; Ztg 5
Zax 10; Ztg 5
Zax 15; Ztg 2.5
Zax 10; Ztg 2.5
Zax 5; Ztg 2.5
Zax 20; Ztg 7.5
Zax 15; Ztg 7.5
Zax 10; Ztg 7.5
Figure 3.5 (a) HFD ratio for different combinations of Zax and Z
tg distances (mm); and (b) these
same HFD ratios multiplied by the term Zax Z
tg
-1
Accuracy and applicability of the HFD method
63
While Steppe et al. (2010) determined a single calibration factor for their species, the
model results show that this will only be sufficient in a certain range of sap flux
densities as no linear relation exists between the ratio and sap flux density.
Therefore, a mathematical relationship should be fitted to the data:
SFD=f(HFD) (3.5)
with HFD the value of the HFD ratio (-), taking into account the influence of needle
spacing, Kax, K
tg, ρ
b and MC as well as the sap flux density dependency of HFD.
Although several relationships can be fitted to the data, a trade off between
goodness of fit and model simplicity (number of parameters to estimate) should be
taken into account. While high order polynomial regressions lead to an acceptable
low sum of squared error, these regressions require a large number of parameters
to be estimated. By running a curve analysis, fitting more than 40 both linear and
non-linear regression functions to the data, the following relationships were
obtained that led to a good fit for all combinations of input thermal properties and
needle distances and had maximum four empirical parameters to estimate:
21
a bHFDSFD
cHFD dHFD (3.6)
d
d
ab cHFDSFD
b HFD (3.7)
2 4
2
a a bHFDSFD
b (3.8)
with a, b, c and d empirical parameters for each equation (Figure 3.6 as an example).
As the HFD ratio is empirical, these parameters will have no strict physical meaning.
Hence, similar as for the TD method (Granier, 1985), the dimensions of these
parameters are not of importance although they can easily be derived from Eq. 3.6,
3.7 and 3.8 as the HFD ratio itself is dimensionless. While for Eq. 3.8 only two
parameters need to be estimated, this fit underestimates lower flows and
overestimates higher flows and should, hence, be avoided. As the standard error for
Eq. 3.6 (1.840) is systematically higher than for Eq. 3.7 (0.280), the latter is
preferred.
Chapter 3
64
To determine this correction equation, a validation experiment similar as done by
Steppe et al. (2010) could be set up. This way, both the non-linearity of the HFD
ratio and its dependency on wood properties are taken into account while the
advantages of the original HFD ratio, namely its sensitivity in a wide range of sap
flux densities and the possibility to establish a radial profile, remain.
These findings raise the question as to what extent results mentioned in previously
conducted studies applying the HFD method are correct. As has been shown by
Steppe et al. (2010), Eq. 2.3 can lead to large underestimations of sap flux density.
These underestimations will, however, be largely dependent on the applied Lsw
value
and, to a smaller extent, on the thermal properties of the sapwood, making error
estimations difficult as these values are often unknown. In general,
underestimations of up to 50% can be expected (Steppe et al., 2010), which is of
importance if absolute water use of trees was investigated. Fortunately, most
research has been focussing on relative flow patterns within the low to moderate
flow range to study phenomena such as radial flow, xylem structure and
Figure 3.6 Mathematical relation between sap flux density and modelled HFD ratio with
a=0.0207, b=0.0028, c=-0.603, d=8.650, e=239, f=0.543, g=4.562, h=24.01, i=0.282, j=-
0.00258 (Kax=0.75 W m-1 K-1, K
tg=0.65 W m-1 K-1, ρ
d=550 kg m-3, MC=0.85).
Accuracy and applicability of the HFD method
65
functionality and hydraulic redistribution. Even though relative deviations must
have occurred, due to the non-linearity of the HFD ratio, the presented patterns are
clear and distinct and, hence, the conclusions correct.
3.5 Conclusions
Although the HFD method has proven its use in many studies because of its
sensitivity towards low, high and reverse flows and the possibility to measure flow
at different depths, the thermal diffusivity in its original equation is often wrongly
interpreted. Therefore, the method should be considered entirely empirical rather
than semi-empirical as the link between the empirical temperature ratio and sap
flux density is not based on fundamental thermodynamics. To enable accurate sap
flux density estimations from the HFD ratio, mathematical relations were derived
which necessitate species-specific calibration. This can be done by forcing a range of
sap flux densities on a cut stem segment and comparing the HFD results with the
gravimetric reference data. This calibration procedure is, however, impractical for
large scale field measurements. Therefore, heat pulse methods seem preferential as
they do not require specific calibrations and, as indicated in Chapter 2, are not
susceptible to NTG.
67
4 4 The anisotropic heat conduction-
convection equation as basis for
heat pulse sap flow methods
After: Vandegehuchte, M.W. & Steppe, K. (2012). Use of the correct heat
conduction-convection equation as basis or heat pulse sap flow methods in
anisotropic wood. Journal of Experimental Botany, 63: 2833-2839.
Abstract
Heat pulse methods to determine sap flux density in trees are based on the theory
of heat conduction and convection in an isotropic medium, with thermal properties
of the medium not directionally differing. However, sapwood is clearly anisotropic,
implying a difference in thermal conductivity along and across the grain, and hence
necessitates the theory for an anisotropic medium. This difference in thermal
conductivities, which can be up to 50 %, is however not taken into account in the key
Chapter 4
68
equation leading to the currently available heat pulse methods. Despite this flaw,
these methods remain theoretically correct as they are based on derivations of the
key equation, ruling out any anisotropic aspects. Nevertheless, it remains important
to specify the thermal characteristics of the sapwood according to axial, tangential
or radial direction and to refer to and use the proper anisotropic theory. This will
avoid confusion and misinterpretation of thermal properties when dealing with sap
flux density measurements or erroneous results when modelling heat transport in
sapwood.
4.1 Introduction
If heat pulse based sap flow methods are based on a theory only applicable for
isotropic materials, not differentiating between directionally different thermal
properties, can they then be accurate for an anisotropic material such as sapwood in
which axial thermal conductivity differs from tangential thermal conductivity? This
chapter will answer this pertinent question by summarizing and comparing the heat
pulse theory for both isotropic and anisotropic media.
Heat pulse methods are based on the theoretical background for heat flow in
sapwood as developed by Marshall (1958) based on the work of Carslaw & Jaeger
(1947). This theory is based on the analytical solution of the partial differential
equation for combined conduction and convection of heat in a specified medium. If
this equation can be solved for the convection term, the velocity by which heat
transfers through the medium, such as sapwood, can be determined and from this,
sap flux density can be calculated.
For the application of an instantaneous line source of heat along the z-axis in an
isotropic medium, the following analytical solution is obtained:
( )² ²exp
4 4
hTx V t yQ
TDt Dt
(4.1)
with ∆T (K) the difference between the temperature at position (x,y) before
application of the heat pulse and a time t (s) after application of the heat pulse, QT
(K m²) defined as the temperature to which the amount of heat liberated per unit
length of the line would raise a unit volume of the substance, D the thermal
Anisotropic theory for heat pulse methods
69
diffusivity (m² s-1) and Vh the heat pulse velocity (m s-1). This heat pulse velocity is
directly proportional to sap flux density according to Eq. 2.4.
It is this equation that was used by Marshall (1958) and many others (Cohen et al.,
1981; Swanson & Whitfield, 1981; Swanson, 1983; Green & Clothier, 1988; Burgess et
al., 2001a) as the basis for the development of heat pulse based sap flow
measurement methods.
4.2 Assumption of isotropic medium versus actual
anisotropic sapwood
Sapwood, however, is composed of conductive elements which main goal is axial
transport. Hence, the structure and thermal properties of sapwood differ according
to the directional orientation, whether axial or tangential. Marshall (1958) already
stated that dry wood is not isotropic, but has a greater thermal conductivity along
the grain (Kax) than across the grain (K
tg). He also acknowledged that wet wood might
also be anisotropic, although probably to a lesser extent. For fresh wood segments
with a water content higher than the fibre saturation point, the axial thermal
conductivity (Kax) can be up to two times larger than the radial (K
rad) or tangential
(Ktg) conductivity, depending on wood species (Maku, 1954; Steinhagen, 1977).
Moreover, when applying the equations as mentioned in Swanson (1983) based on
the work of Turrell et al. (1967) and Siau (1971) for the calculation of Kax and K
tg, it is
clear that Ktg (and hence thermal diffusivity, D
tg) is remarkably smaller across all dry
wood densities and water contents with Ktg on average (54±7.5) % of K
ax (Figure 4.1).
This approach was also applied by Burgess et al. (2001a) to determine axial thermal
diffusivity (Dax) for the Heat Ratio method (see Chapter 5).
Chapter 4
70
When considering anisotropy, the analytical solution of the partial differential
equation for combined conduction and convection of heat, from which Eq. 4.1 was
derived for isotropic media, becomes:
( )² ²exp
44
hT
ax tgax tg
x V tQ c c yT
t K KK K t (4.2)
And it is, hence, this equation (Eq. 4.2) that should be the key equation for sap flow
measurements based on pulsed heating by an ideal line heater instead of Eq. 4.1
which has, so far, been used as reference equation.
4.3 Implications of anisotropy for current sap flow
methods
Applying Eq. 4.1 and 4.2 for heat transport in sapwood with a given dry wood
density and water content and the same heat input, clearly leads to different
Water content (kgwater
kgdry wood
-1)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Th
erm
al co
nd
uctivity (
W m
-1 K
-1)
0.0
0.2
0.4
0.6
0.8
1.0d = 1050 kg m
-3
d = 900 kg m-3
d = 750 kg m-3
d = 500 kg m-3
d = 350 kg m-3
Figure 4.1 Axial (black lines) and tangential (grey lines) thermal conductivities for different
water contents and dry wood densities (ρb) as calculated according to Turrell et al. (1967))
based on Siau (1971).
Anisotropic theory for heat pulse methods
71
temperature patterns in the wood (Figure 4.2). These different patterns are caused
bydifferences in thermal diffusivity, with the isotropic diffusivity taken as the
geometric mean of the axial and tangential diffusivity (Figure 4.3). This also affects
the parameters used in the methods based on Eq. 4.1 to determine sap flux density,
such as the Tmax method and the Heat Ratio method. For the Tmax method, the
difference in temperature field results in a difference in tm (Figure 4.4a), while for
the Heat Ratio method, the ratio (∆Tdown
/∆Tup
) is clearly influenced (Figure 4.4b).
Time (s)
0 50 100 150 200 250 300
Tem
pera
ture
(°C
)
19.8
20.0
20.2
20.4
20.6
20.8
21.0
21.2
Tdown anisotropic
Tup anisotropic
Ttg anisotropic
Tdown isotropic
Tup isotropic
Ttg isotropic
Figure 4.2 Temperatures at 6 mm axially downstream, upstream and tangentially from the
heater for a water content of 70% and dry wood density of 550 kg m-3. For the isotropic case,
the thermal diffusivity D was taken as the geometric mean of Dax and D
tg of the anisotropic
case.
Chapter 4
72
If Eq. 4.1 is not valid for sapwood with anisotropic thermal conductivity, does this
imply that the methods based on this equation are not applicable? Not necessarily,
because most methods are based on derivations from Eq. 4.1. Marshall (1958) based
Water content (kgwater
kgdry wood
-1)
0.7 0.9 1.1
Th
erm
al d
iffu
siv
ity s
ap
wo
od
(m
2 s
-1)
0.0
5.0e-8
1.0e-7
1.5e-7
2.0e-7
2.5e-7
3.0e-7
3.5e-7
Axially
Tangentially
isotropic
Vh (cm h-1)
0 20 40 60 80 100 120 140 160 180
t m (
s)
10
20
30
40
50
MC 70%, anisotropic
MC 70%, isotropic
MC 90%, anisotropic
MC 90%, isotropic
MC 110 %, anisotropic
MC 110%, isotropic
Vh (cm h-1)
0 20 40 60 80 100 120 140 160 180
T
dow
n/
Tup)is
otro
pic
/( T
dow
n/
Tup)a
nis
otro
pic
0
2
4
6
8
10
12
14
MC 70%
MC 90%
MC 110%
(a) (b)
Figure 4.3 Thermal diffusivities for both the isotropic and anisotropic case for different water
contents. The dry wood density was taken as 550 kg m-3. The isotropic thermal diffusivity was
taken as the geometric mean of Dax and D
tg of the anisotropic case.
Figure 4.4 (a) Time to maximum (tm) values and (b) ratio of the HR method temperature ratio
(∆Tdown
/∆Tup
) for isotropic and anisotropic sapwood with different water contents. The isotropic
thermal diffusivity D was taken as the geometric mean of Dax and D
tg of the anisotropic case.
Anisotropic theory for heat pulse methods
73
his measurements of Vh and D on the substitution of two points on the temperature-
time curve (t1,T
1) and (t
2,T
2):
1 21 1
2 2 1 1 2 2
( )² ( )²² ²ln
4 4 4 4
h h
ax tg ax tg
c x V t c x V tT t cy cy
T t K t K t K t K t
(4.3)
If the measurement point is now chosen at an axial distance x (with y=0), this
becomes:
1 1 1 21 2
2 2 1 2
( )²ln ( ² ² )
4h
ax
T t c t tx V t t
T t K t t
(4.4)
or
1 1 1 21 2
2 2 1 2
( )²ln ( ² ² )
4h
ax
T t t tx V t t
T t D t t
(4.5)
When applying this equation to two other points t3 and t
4 so that t
1+t
4=t
2+t
3=2t
2, a
similar equation is obtained, leading to two equations with two unknown variables:
Dax and V
h. These equations can then easily be solved to obtain expressions for both
Dax and V
h. If the same mathematics are applied on Eq. 4.1, the same result is
obtained which makes clear that the thermal diffusivity as calculated by Marshall
(1958) really is the axial thermal diffusivity (Figure 4.5). Hence, by locating the
measurement needles only in the axial direction and choosing specific data points
on the temperature-time curve, the difference introduced by anisotropy between Eq.
4.1 and 4.2 is ruled out. This is also the case for the Heat Ratio method (Burgess et
al., 2001a). Here, the same distances of the axial measurement points upstream and
downstream from the heater needle were applied which also negates the difference
between axial and tangential conductivity (Figure 4.6).
Chapter 4
74
Heat conduction-convection equation
Isotropic Anisotropic
Marshall’s solution
Applying only axial measurements
ax tg rad h
T T T T Tc K K K cV q
t x x y y z z x
2 2( )exp
4 4
hT x V t ycQT c
Kt Kt
2 2( )exp
44
hT
ax tgax tg
x V tcQ c yT
t K KK K t
2 2 2 2
1 21 1
2 2 1 2
( ) ( )ln
4 4
h hx V t y x V t yT tc c
T t Kt Kt
21 1 1 22 1 2
2 2 1 2
( )ln
4h
T t c t tx V t t
T t Kt t
21 1 1 22 1 2
2 2 1 2
( )ln
4h
T t t tx V t t
T t Dt t
2 22 2
1 21 1
2 2 1 1 2 2
( ) ( )ln
4 4 4 4
h h
ax tg ax tg
x V t x V tT t y yc c c c
T t K t K t K t K t
21 1 1 21 2
2 2 1 2
( )ln
4h
ax
T t c t tx V t t
T t K t t
21 1 1 21 2
2 2 1 2
( )ln
4h
ax
T t t tx V t t
T t D t t
Heat conduction-convection equation
Isotropic Anisotropic
Burgess’ solution
Applying only axial measurements and choosing x1=-x2
ax tg rad h
T T T T Tc K K K cV q
t x x y y z z x
2 2( )exp
4 4
hT x V t ycQT c
Kt Kt
2 2( )exp
44
hT
ax tgax tg
x V tcQ c yT
t K KK K t
2 2 2 211 2 1 2 2 1
2
ln 2 ( )4
h
T cx x y y V t x x
T Kt
2 2 2 2
1 1 2 1 22 1
2
2ln ( )
4
h
ax tg ax
V tT x x y ycx x
T t K K K
2
2
lnh
TKV
cx T
2
2
lnh
TDV
x T
2
2
lnaxh
K TV
cx T
2
2
lnaxh
D TV
x T
Figure 4.5 Marshall’s solution of Eq. 4.1 to determine Vh and D
ax (Marshall, 1958). By using
only axial measurements and substituting specific points of the temperature-time curve, the
influence of anisotropy is ruled out. Similar equations can be developed for t3 and t
4 to obtain
two equations including Vh and D
ax which can then be determined.
Figure 4.6 Burgess’ solution of Eq.4.1, based on Marshall (1958), to determine Vh. By
measuring on specific distances upstream and downstream of the heater (x1=-x
2), the actual
axial conductivity is applied, even when starting from the isotropic theory.
Anisotropic theory for heat pulse methods
75
This also holds for the Tmax method of Cohen et al. (1981) (Figure 4.7). Even though
thermal diffusivity is mentioned in this work as D in Eq. 4.1, in practice Dax is being
measured. By using the derivative of Eq. 4.1 for a measurement needle located
axially from the heater, correct equations for both Dax during conditions of zero flow
and Vh are obtained:
2
4ax
m
xD
t (4.6)
2 4 ax m
h
m
x D tV
t
(4.7)
with tm the time at which ∆T is maximal. D
tg can be determined when measuring the
temperature curve at a tangential distance (0,y) from the heater needle (Figure 4.7):
2
4tg
m
yD
t (4.8)
Note that it is incorrect to apply any distance d as mentioned in Cohen et al. (1981)
(Eq. 2.6, 2.7) as a distinction between axial and tangential distances needs to be
made to obtain the corresponding diffusivities.
Also for the Compensation Heat Pulse method, the isotropic and anisotropic theory
lead to the same heat velocity results as the intersection point between upstream
and downstream temperature profiles remains constant. Hence, it can be concluded
that currently existing heat-pulse sap flux density measurement methods remain
valid, even though they are based on an inaccurate theory, as by mathematical
manipulations the same results are obtained as if the correct anisotropic theory
would have been applied. It is now also clear that these methods determine the
actual axial thermal diffusivity and not a mean of axial and tangential or overall
thermal diffusivity as is sometimes mistakenly thought.
Chapter 4
76
Heat conduction-convection equation
Isotropic Anisotropic
Cohen’s solution
Applying only axial measurements
Applying only tangential measurements
ax tg rad h
T T T T Tc K K K cV q
t x x y y z z x
2 2( )exp
4 4
hT x V t ycQT c
Kt Kt
2 2( )exp
44
hT
ax tgax tg
x V tcQ c yT
t K KK K t
2 2 4 m
h
m
Ktx y
cV
t
2 4 m
h
m
Ktx
cV
t
2
04
h
m
K xIf V D
c t
2 4 m
h
m
Kty
cV
t
2
04
h
m
K yIf V D
c t
2 2 4ax ax m
tg
h
m
K K tx y
K cV
t
2 4 ax m
h
m
K tx
cV
t
2
04
axh ax
m
K xIf V D
c t
2
2
4 ax tg m
ax
h
tg m
K K tK y
cV
K t
2
04
tg
h tg
m
K yIf V D
c t
The difference in Dax and D
tg (or K
ax and K
tg) must also be made when numerical
models are used to assess heat pulse measurement systems based on Eq. 4.1. This
difference was taken into account by using the method of mixtures of Turrell et al.
(1967) in combination with the determination of dry wood thermal conductivity by
Siau (1971) in both the work of Swanson (1983) and Green, Clothier & Jardine (2003)
for their FEM to assess the errors of several heat pulse methods. In earlier work of
Swanson & Whitfield (1981), the axial conductivity was taken as twice the tangential
conductivity, independent of wood water content and, hence, only partially
accounting for the differences between Kax and K
tg.
However, in Jones, Hamer & Higgs (1988) this difference was overlooked. These
authors correctly stated that all heat pulse methods could benefit from the use of
curve-fitting procedures, but directly implemented Eq. 4.1, thereby neglecting the
anisotropy of the sapwood. This error was also made by Becker (1998) for a
theoretical example and, more recently, by Chen et al. (2012) in their statistical
method to determine probe spacing and wood thermal diffusivity. As these authors
did not differentiate between axial and tangential thermal diffusivity, their
numerical analyses need to be reconsidered. Next to these known examples, perhaps
Figure 4.7 By differentiating Eq. 4.1 to determine the time at which the maximal ∆T occurs, a
solution for Vh is obtained. When applying only axial measurements, the actual axial thermal
conductivity is used for these calculations
Anisotropic theory for heat pulse methods
77
others have made the same mistake, erroneously implementing Eq. 4.1 instead of
4.2.
4.4 Towards more accurate equations
Eq. 4.1, for an isotropic, and Eq. 4.2, for an anisotropic medium, are valid for
instantaneous pulses only, which is however never the case in practice. Both
Swanson (1983) and later Kluitenberg & Ham (2004) noted that for pulses longer
than 2 seconds, application of the instantaneous pulse theory can lead to important
errors (up to 10%) in determination of thermal diffusivity and sap flux density.
Therefore, it was suggested to implement the theory applicable for a step pulse. For
an anisotropic medium, this results in following equations:
1
0
( )² ²exp
44
t
h
ax tgax tg
x V tq c yT t dt
t K KK K for 0<t<=t
0 (4.9)
0
1 ( )² ²exp
44
th
t tax tgax tg
x V tq c yT t dt
t K KK K for t
0<t (4.10)
where q (W m-1) is the amount of heat liberated per unit length of the heater per
time. Eq. 4.9 and 4.10 can be numerically solved. When differentiating Eq. 4.10 to
time, similarly as was done by Cohen et al. (1981) for an instantaneous pulse, both
Dax and D
tg can be determined. We tested this method on a cut segment of European
beech (Fagus sylvatica L.) for several gravimetrically determined water contents by
positioning two sensor needles at 7.5 mm from the heater, respectively axially and
tangentially (Figure 4.8). The results confirm an important difference between Dax
and Dtg. Not only is D
ax 1.8 to 2.3 larger than D
tg, it is also more influenced by the
water content of the sapwood.
Chapter 4
78
4.5 Conclusion
Throughout literature on heat pulse based sap flow measurement methods, there
seems to be an inconsistency when referring to thermal diffusivity of sapwood.
Despite clear evidence that sapwood is an anisotropic material for which axial
diffusivity Dax and tangential diffusivity D
tg will be markedly different, thermal
diffusivity is often addressed as an overall diffusivity for the whole material, based
on Eq. 4.1 (Marshall, 1958; Cohen et al., 1981; Jones et al., 1988; Cohen et al., 1993;
Becker, 1998; Nadezhdina et al., 1998; Burgess et al., 2001a; Green et al., 2003; Bleby
et al., 2004; Kluitenberg & Ham, 2004; Green et al., 2009). Nevertheless, the existing
heat pulse based sap flow methods are still theoretically correct and yield actual Dax
values due to their reliance on derivations of Eq. 4.1 and the use of only axial needle
positioning. However, when applying Eq. 4.1 for numerical modelling or for other
purposes for which the mathematical derivations do not cancel out the isotropic
effect, this will lead to errors in both diffusivity and sap flux density calculations.
To avoid further confusion and prevent mistakes in future research, we suggest to
mention Eq. 4.2 when referring to the development of heat pulse sensors and to
consequently discriminate between axial or tangential thermal diffusivity and/or
Water content (kgwater
kgdry wood
-1)
0.4 0.5 0.6 0.7 0.8 0.9 1.0
Th
erm
al d
iffu
siv
ity (
cm
2 s
-1)
0.0010
0.0012
0.0014
0.0016
0.0018
0.0020
0.0022
0.0024
0.0026
0.0028
0.0030
Dax
Dtg
Figure 4.8 Axial and tangential thermal diffusivity for European beech at different water
contents calculated in analogue with the Tmax method (Cohen et al., 1981) but applied for a
step heat pulse (Eq. 4.9 and 4.10)
Anisotropic theory for heat pulse methods
79
conductivity. Furthermore, we encourage the use of Eq. 4.9 and 4.10, because they
will be more accurate than those based on the instantaneous pulse theory.
Besides derivations from the heat conduction-convection equation, another way to
determine Dax is to apply the method of mixtures mentioned in Turrell et al. (1967)
in combination with the dry wood thermal conductivity determinations of Siau
(1971) which was specifically derived for the axial and tangential direction. The next
chapter, however, shows that in this method, sapwood water content was wrongly
interpreted, making it incorrect as the fibre saturation point is not taken into
account.
81
5 5 Differentiating between bound and
unbound water in the method of
mixtures for diffusivity calculation
After: Vandegehuchte, M.W & Steppe, K. (2012). Improving sap flux
density measurements by correctly determining thermal diffusivity,
differentiating between bound and unbound water. Tree Physiology, 32: 930-
942
Abstract
Several heat-based sap flow methods, such as the Tmax and the Heat Ratio method,
include the axial thermal diffusivity Dax of the sapwood as a crucial parameter.
Despite its importance, little attention has been paid to determine Dax in a plant
physiological context. Therefore, Dax is mostly set as a constant, calculated during
Chapter 5
82
zero flow conditions or from a method of mixtures, taking into account wood
density and water content. In this latter method, however, the meaning of the water
content is misinterpreted, making it theoretically incorrect for Dax calculations in
sapwood. A correction to this method, which includes the correct application of the
water content, is proposed. This correction was tested for European and American
beech and Eucalyptus caliginosa Blakely & McKie. Depending on the dry wood
density and water content, the original approach over- or underestimates Dax and,
hence, sap flux density by 10 % and more.
5.1 Introduction
While the Compensation Heat Pulse method (Swanson & Whitfield, 1981; Green &
Clothier, 1988) operates independent of the axial thermal diffusivity Dax of the
sapwood, for the Heat Ratio and the Tmax method, (Marshall, 1958; Cohen et al.,
1981; Burgess et al., 2001a; Clearwater et al., 2009), Dax is a crucial parameter to
determine sap flux density. As in the HR equation Dax is directly linearly
proportional to sap flux density, an error of x % will lead to an equal error in sap
flux density and, hence, calculated sap flow. This high linear sensitivity of sap flow
measurements towards Dax has been reported in the sensitivity analysis of Steppe et
al. (2010). For the Tmax method, the influence of Dax on sap flux density is less
straightforward. The sensitivity analysis of Cohen et al. (1981) indicates that a 10 %
error in Dax only leads to a maximal error of 3 % in sap flux density for a probe
spacing of 5 mm and even smaller for larger probe spacings.
Despite its importance as parameter in sap flow calculations, little attention has
thus far been paid to characterize Dax in a plant physiological context. Most research
has been done on wood that is used as construction material and the results are
therefore only applicable for dry wood samples. These dry samples have a water
content MC, calculated as the ratio of the weight of water divided by the dry weight
of the sapwood, below the point where only bound water is present (fibre saturation
point, FSP) (Harada et al., 1998; Suleiman et al., 1999; Adl-Zarrabi et al., 2006).
Simpson & TenWolde (1999) state that Dax measurements for water content values
above 25 % are few in number and generally lack accuracy. As the water content in
sapwood of living trees ranges between 98% to 249 % for conifers and between 44 %
Interpreting MC in D determination
83
and 162 % for hardwoods, dependent on species and seasonality (Skaar, 1988), there
clearly is a lack in Dax knowledge for sap flow applications.
As explained in section 4.3, Marshall (1958) determined Dax by applying Eq. 4.2 for
specific times after application of the heat pulse, mentioning a range of 0.0014 to
0.0040 cm2 s-1. These values are based on the equations for an ideal heat pulse. In
addition, this method seems impractical as the four used time points need to be
specifically chosen to reach the requisite of t1+t
4=t
2+t
3=2t
2. For the Tmax method, the
weaknesses are that zero flow conditions are required and that it is based on one
time point which is difficult to determine as the measured temperatures during zero
flow have a broad peak, impeding the determination of tm (Green et al., 2003). The
method as mentioned in Burgess et al. (2001a) based on the work of Swanson
(1983), Turrell et al. (1967) and Siau (1971) is not dependent on point measurements
of temperatures after application of a heat pulse nor on zero flow conditions as a
sample is taken from the sapwood, but determines Dax based on an empirical
relationship for which only a fresh wood sample needs to be taken. Given the
growing popularity of the HR method, this approach to determine Dax has been
frequently applied. Table 5.1 gives an overview of recent papers in which thermal
diffusivity was calculated accordingly. From the 43 papers investigated, 29
mentioned the application of the method as described in Burgess et al. (2001a),
while 11 did not mention it specifically, but did apply HR measurements to quantify
sap flow. Hence, it is assumed that in these studies, the method was also applied. In
only 3 papers, the HR method was used relatively, pre-empting the use of thermal
diffusivity.
Chapter 5
84
Year published Publications in which Dax is determined according to Burgess et
al. (2001a)
2011 Hernandez-Santana et al. (2011); Staudt et al. (2011)
2010 Ambrose et al. (2010); Bleby et al. (2010); Er-Raki et al. (2010):
Macfarlane et al. (2010); MCElrone et al. (2010); Miller et al.
(2010); Pfautsch et al. (2010); Zeppel et al. (2010)
2009 Hao et al. (2009); Hu et al. (2009); Madurapperuma et al.
(2009a; 2009b); Mitchell et al. (2009); O'Grady et al. (2009);
Pfautsch et al. (2009); Turnipseed et al. (2009); Winters et al.
(2009)
2008 Moore et al. (2008); Scott et al. (2008); Zeppel et al. (2009)
2007 Fisher et al. (2007); MCElrone et al. (2007); Scholz et al.
(2007); Warren et al. (2007); West et al. (2007)
2006 Burgess & Bleby (2006); Langensiepen et al. (2006)
2005 Oliveira et al. (2005)
2004 Bleby et al. (2004); Bucci et al. (2004); Burgess & Dawson
(2004); Hultine et al. (2004); Williams et al. (2004)
2003 Hultine et al. (2003a; 2003b); Kurpius & Goldstein (2003);
Kurpius et al. (2003); Yepez et al. (2003)
2002 Scholz et al. (2002)
Table 5.1 An overview of literature in which the Heat Ratio method is applied. For 40 papers,
thermal diffusivity is calculated according to the approach mentioned in Burgess et al. (2001).
Interpreting MC in D determination
85
5.1.1 But are we missing the point when applying the thermal diffusivity
theory?
Although the recalculation based on fresh/dry sapwood density and water content
determined from a sapwood sample is currently considered as the way to determine
Dax in sap flow research (Burgess et al., 2001a), the underlying theory is incorrect for
sapwood with water contents above the fibre saturation point which is the case for
most, if not all, transpiring trees during sap flow measurements. The approach
proposed by Burgess et al. (2001a) applies the method of mixtures as mentioned in
Skaar (1988) to determine c (J kg-1 K-1) of wet wood:
( )d d w f d
f
w c c w wc
w
(5.1)
where wf is the fresh and w
d the oven-dried weight of a wood sample (kg) and c
w and
cd the specific heat capacity of water (4186 J kg-1 K-1) and dry wood (1200 J kg-1 K-1) at
20°C, respectively (Edwards & Warwick, 1984). This method is known to
underestimate c of wet wood because the energy in the wood-water bonds is not
taken into account (Kelsey & Clarke, 1956). These authors state that this could lead
to differences up to 10 %. Morton & Hearle (1975) highlighted that c of sorbed water
itself is lower than that of free liquid water. This was however not taken into
account in the calculations of Kelsey & Clarke (1956) nor in the calculation of
Hearmon & Burcham (1955) as they used the same c for both free and bound water.
Nevertheless, bound water, when the water content exceeds the fibre saturation
point (MCFSP
), generally accounts for about 30 % of the total water expressed as water
mass per dry wood mass (Siau, 1984), although this value can be higher for low dry
wood densities and lower for high dry wood densities (Skaar, 1988). It is thus
difficult to conclude if this manner of determining c will lead to over- or
underestimations for sapwood, which generally contains high percentages of free
water. However, the method of mixtures is generally considered as a reliable
calculation procedure (Stamm & Loughborough, 1935; Steinhagen, 1977).
Similarly as for c, a method of mixtures, modified from Turrel et al. (1967) and also
mentioned in Swanson (1983), is used to determine axial thermal conductivity Kax (W
m-1 K-1):
Chapter 5
86
d d
w w
ρ ρ1
ρ ρ
ax w dK K MC K MC (5.2)
with Kw and K
d the thermal conductivity of water (0.5984 W m-1 K-1) and dry wood at
20°C, MC the water content of the sample (ratio of water weight to dry wood weight)
and ρw and ρ
d the densities of water and dry wood (kg m-3). To determine K
ax of dry
wood (Kd), an equation based on a theoretical model developed by Siau (1971) is
used:
Kd=0.04186 (21.0-20.0F
v) (5.3)
with Fv the void fraction of the wood. This equation was obtained by a single-cell
model with cell dimensions of unity length, width and height and an internal lumen
with a length and width of dimension a (=√Fv) (Figure 5.1). For a flux in the direction
of the fibre axis, Kd becomes:
Kd=K
mx(1-F
v)+K
airF
v (5.4)
with Kmx
the (axial) thermal conductivity of the (wet) wood matrix and Kair
the
thermal conductivity of air. To obtain Eq. 5.3, Eq. 5.4 was fitted to Kd data found in
literature and a good agreement was obtained when using 0.0001 cal cm-1 s-1 K-1
(0.04186 W m-1 K-1) for Kair
and 0.0021 cal cm-1 s-1 K-1 (0.8791 W m-1 K-1) for Kmx
(Siau,
1971). Thus far, the method seems theoretically sound, neglecting similar
implications of using a mixed-model as for the determination of c. However, the
conductivity single-cell model of Siau (1971) is based on a combination of K of cell
wall material (with a certain water content) and an air filled lumen without unbound
water. Hence, the model was developed for non-saturated wood.
Interpreting MC in D determination
87
In this model, the void fraction is defined as:
Fv=1-G((ρ
w/ρ
cw)+MC) (5.5)
with G the specific gravity of wood (dry mass per fresh volume divided by the
density of water) at water content MC (moisture per dry weight), ρcw
the cell wall
density (1530 kg m-3, Kollmann and Côté (1968)) and ρw the sap (=water) density
(1000 kg m-3). This void fraction thus indicates the volume fraction of air in the
wood. Interestingly, this expression is valid for water contents below the fibre
saturation point. When deducing Eq. 5.4 from the conductivity single-cell model,
Siau (1971) highlighted that Kd is not independent of MC. He reasoned that an
increase in water content decreases the porosity Fv of the wood resulting in an
increase in Kd. This reasoning is however an oversimplification of reality, as the rise
in Kd will not only be due to a decrease in porosity but also due to the fact that the
thermal conductivity of (bound) water is higher than that of completely dry wood
components without water or air (0.10512 W.m-1.K-1 according to Stamm (1964)).
Nevertheless, for practical purposes of wood that is used as a construction material,
Siau (1971) concluded that Kmx
can be considered independent of MC. The fit of
experimental data to Eq. 5.4 led to small deviations for MC ranging from 0 to 25 %,
Figure 5.1 Geometrical model for a single wood cell on which the theory of Siau (1971) is
based, with L the length and width of the wood cell and a the length and width of the internal
lumen.
Chapter 5
88
justifying his assumption. This fit led to the value of 0.0021 cal cm-1 s-1 K-1 for Kmx
and Eq. 5.3.
However, the main implication of the use of this model in sap flow research lays in
the interpretation of MC. In the first part of Eq. 5.2, describing the contribution of
water to the total thermal conductivity, MC is used as a measure for the amount of
free water. In the second part of Eq. 5.2, describing the contribution of dry wood,
the same MC is used. The conductivity Kd, however, already takes into account the
water bound in the wood matrix. This implies that MC ascribed to free water will be
smaller than total MC calculated as the difference between fresh weight and oven-
dry weight divided by the fresh weight of a sample. Moreover, the void fraction Fv
represents the void fraction at fibre saturation point which will be larger than the
void fraction at higher water contents.
5.1.2 Corrected equation to determine thermal conductivity Kax
For a correct application of the concept, Eq. 5.4 should be used to calculate the total
thermal conductivity for MC below the fibre saturation point as was intended by
Siau (1971). For higher MC, the following equation should be used:
d_
w
ρ( ) (1 )
ρax w FSP mx v FSP air vK K MC MC K F K F (5.6)
with MCFSP
the water content at fibre saturation point and Fv_FSP
equal to 1-G((ρ
w/ρ
cw)+
MCFSP
), the volume fraction at fibre saturation point. However, here Kmx
and Kair
will
not hold the same value as in Eq. 5.4 as the applied volume fractions differ. Hence,
the empirical derived coefficients as determined by Siau (1971) are no longer
applicable. Therefore, it will be assumed that Fv in Eq. 5.6 is equal to F
v_FSP. This will
only induce an overestimation in Kax of a few percent given the small thermal
conductivity of air compared to total wood thermal conductivity. Hence, the
equation becomes:
d_ _
w
ρ( ) (1 )
ρax w FSP mx v FSP air v FSPK K MC MC K F K F
or
Interpreting MC in D determination
89
d_
w
ρ( ) 0.04186(21.0 20.0 )
ρ ax w FSP v FSPK K MC MC F (5.7)
Eq. 5.7 is more correct in determining thermal diffusivity in sapwood compared to
Eq. 5.2 which has thus far been used. The objectives of this chapter are to estimate
the errors in thermal diffusivity and sap flux density across varying wood properties
due to application of the erroneous Eq. 5.2 which does not distinguish between
bound and unbound water in sapwood.
5.2 Materials and Methods
5.2.1 Sensitivity analysis
To assess the difference in water use according to current practice for HR
measurements and the results generated using Eq. 5.7, the relative error (SFDerr
) in
sap flux density (SFD) was determined, calculated as the difference between SFD
obtained based on Eq. 5.2 and based on Eq. 5.7, respectively, divided by SFD based
on Eq. 5.7. To gain insight into the influence of the different parameters in Eq. 5.2
and 5.7 on this relative error, the centralized relative sensitivity function of this
relative error SFDerr
towards each parameter θ was calculated as:
( ) ( )( )
2
err errerr
err
SFD SFDS SFD
SFD (5.8)
with ∆θ taken as 1 % of the source component value θ. This way, the relative
sensitivities of SFDerr
to MC, MCFSP
and ρd were calculated. Besides, a sensitivity
measure δmeas similar to that of Brun et al. (2002), Steppe et al. (2006) and De Pauw et
al. (2008) was calculated:
2
,
1
1 Nmeas
i k
k
sN
(5.9)
where k is the sensitivity MC instance, N the number of MC instances for the
sensitivity function and si,k the relative sensitivity of SFD
err to the parameter i of
interest (MC, MCFSP
or ρd). As MC
FSP generally ranges between 15 and 35 %, depending
on wood species (Skaar, 1972), these values were implemented in the simulation. For
dry wood density, Skaar (1972) mentions a range from 310 kg m-3 for Western Red
Chapter 5
90
Cedar up to 1100 kg m-3 for Ceylon Satinwood. Note that ρd also varies within
species, depending on age, height and environmental conditions.
5.2.2 Plant material
To assess the implications of the misinterpretation of the method of Siau (1971) in
the field, experiments were conducted in which wood sections were taken from
European (Fagus sylvatica L.) and American (Fagus grandifolia Ehrh.) beech, both
diffuse-porous hardwoods. Sapwood sections of three 10- to 20-years old European
beech trees were taken at the experimental forest ‘Aelmoeseneie’ of Ghent
University (Gontrode, Belgium) and sections from two 60- to 70-years old American
beech trees were taken from Whitehall forest, the experimental forest of the
University of Georgia (Athens, Georgia, USA). The trees had a stem diameter at
breast height ranging from 14 to 21 cm.
For each cut tree, a sapwood section was taken at breast height. For two of the
European and American beech trees, wood sections were also taken at 50 cm above
breast height. After measuring the fresh weight of these sections, the volume was
determined by immersing the fresh wood sample, tightly wrapped in parafilm
(Parafilm M, SPI supplies/Structure Probe Inc., West Chester, PA 19380, USA) to
avoid water adsorption, in water and applying Archimedes’ principle. Afterwards,
the sections were dried to determine their dry weight. From these measurements,
MC, ρd and F
v and F
v_FPS were determined. Fibre saturation point values were estimated
according to Roderick & Berry (2001):
MCFSP
=0.2 (ρd ρ
w
-1)-1/2 (5.10)
with ρd (kg m-3) the dry wood density and ρw the density of water (1000 kg m-3).
5.2.3 Thermal conductivity versus water content: original versus
corrected method
For one European beech tree, a stem segment of approximately 1 m was cut in the
forest. The ends of this segment were sealed with parafilm (Parafilm M, SPI
supplies/Structure Probe Inc., West Chester, PA, 19380, USA) and enclosed in a
plastic bag to minimize evaporation. After transportation to the Laboratory of Plant
Ecology, Ghent University, a small section of sapwood of approximately 250 cm3 was
cut from the centre of this larger segment. This section was weighed, left to dry and
Interpreting MC in D determination
91
then wrapped in parafilm (Parafilm M, SPI supplies/Structure Probe Inc., West
Chester, PA 19380, USA) for one hour to ensure a homogenous water content. Then
the weight of the section was measured. This was repeated to obtain a range of
water contents from approximately 0.45 to 0.8. Afterwards, the volume of the
section was determined according to the Archimedes’ principle. These
measurements allowed us to establish a relation between thermal conductivity and
water content both for the original and the corrected method.
5.2.4 Implications of the correction for actual sap flow measurements
To assess the implications of an inaccurate estimation of thermal diffusivity due to
a misinterpretation of water content, sap flow in an Eucalyptus caliginosa was
measured using the HR method (Burgess et al., 2001a). From this Eucalyptus
caliginosa, a segment with diameter 9.1 cm was freshly cut, prepared and hung in a
gravimetric validation system similarly as done by Steppe et al. (2010). This way, HR
measured sap flow with the diffusivity calculated according to both Eq. 5.2 and 5.7
could be compared with gravimetric data of sap flow. For this experiment, a
commercially available HR sensor was used, consisting of a heater needle and two
measurement needles located 5 mm upwards and downwards of the heater needle,
respectively (ICT International PTY LTD, Armidale, Australia). For this sensor, the
diameter of the needles is 1.5 mm and their length 35 mm and a wound width of
1.71 mm was determined. In each measurement needle, two thermocouples are
located at respectively 7.5 and 22.5 mm from the needle tip, located respectively 3
and 18 mm below the bark. For these measurements, Dax was calculated according to
both Eq. 5.2 and 5.7. To partially correct for the radial sap flux density profile, also
an HFD sensor (ICT International PTY LTD, Armidale, Australia) was installed
(Steppe et al., 2010). This sensor was installed 10 cm axially upstream and 90°
tangentially from the HR sensor and has the ability to estimate sap flux densities at
eight different depths, with 10 mm between each measurement depth and the first
depth at 3 mm below the bark. Hence, for both sensors, a measurement point is
located at 3 mm below the bark for which the ratio of the HR to the HFD sap flux
density was determined. By multiplying this ratio to the sap flux densities obtained
by the HFD sensor at the other seven depths, a radial profile was calculated based
on the accuracy of the HR measurements (Steppe et al., 2010). Hence, it was possible
to determine the sap flow through the segment more accurately, combining the
Chapter 5
92
relative HFD radial profile with the absolute values of the HR method. As the
measured flows were rather low (<25 cm3 cm-2 h-1), the relative radial sap flux density
pattern of the HFD was assumed to be correct (see Chapter 3).
The fibre saturation point was determined according to Eq. 5.10. A wood section of
19.6 cm3 was taken at the position of the HR sensor from which fresh weight, dry
weight and volume were determined, necessary to calculate thermal diffusivity.
5.3 Results
Figure 5.2 shows the results of applying Eq. 5.2 and 5.7 for different dry wood
densities (ρd) and fibre saturation points (MC
FSP) over a wide range of water contents.
In Figure 5.3, the relative error in sap flux density (SFDerr
) due to the application of
Eq. 5.2 instead of Eq. 5.7 is given for these same sapwood parameters. The
corresponding relative sensitivities of SFDerr
to MC, MCFSP
and ρd are presented in
Figure 5.4 while Figure 5.5 represents the sensitivity measures δmeas.
Water content (kgwater
kgdry wood
-1)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
The
rmal con
du
ctivity K
ax (
W m
-1 K
-1)
0.0
0.2
0.4
0.6
0.8
1.0
Kax Eq. 5.7 MCFSP 0.15
Kax Eq. 5.7 MCFSP 0.25
Kax Eq. 5.7 MCFSP 0.35
Kax Eq. 5.2
d 1100 kg m-3
d 850 kg m-3
d 600 kg m-3
d 350 kg m-3
Figure 5.2 Application of Eq. 5.2 and 5.7 for different dry wood densities (ρd). For Eq. 5.7, fibre
saturation points ranging between 15 and 35% were implemented (striped gray lines). For
each ρd, thermal conductivity K
ax increases for rising fibre saturation points.
Interpreting MC in D determination
93
Moisture content (kgwater
kgdry wood
-1)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Re
lative
sa
p f
lux d
en
sity e
rro
r
-0.2
-0.1
0.0
0.1
0.2
0.3
MCFSP 0.15
MCFSP 0.25
MCFSP 0.35
d 350 kg m-3
d 600 kg m-3
d 850 kg m-3d 1100 kg m
-3
Rela
tive s
ensitiv
ity
to r
ela
tive s
ap f
lux d
ensity
err
or
SF
De
rr
-0.6
-0.4
-0.2
0.0
MCFSP 0.15
MCFSP 0.25
MCFSP 0.35
Water content (kgwater kgdrywood
-1)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
-0.6
-0.4
-0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(a) (b)
(c) (d)
MC
MCFSP
d MC
MC
MC
MCFSP
MCFSPMCFSP
d
d
d
Figure 5.3 The relative error in sap flux density, calculated as the ratio of the difference
between sap flux density applying Dax based on Eq. 5.2 and based on Eq. 5.7,
respectively, to the sap flux density applying Dax based on Eq. 5.7, for different water
contents
Figure 5.4 Relative sensitivities of the relative error in sap flux density (SFDerr
) to water
content (MC), fibre saturation point (MCFSP
) and dry wood density (ρd) for ρ
d 350 kg m-3
(a), 600 kg m-3 (b), 850 kg m-3 (c) and 1100 kg m-3 (d).
Chapter 5
94
Table 5.2 shows the water content, dry wood density and corresponding thermal
conductivity according to Eq. 5.2 and Eq. 5.7 for both the European and the
American beech sections. The percentage over- or underestimation due to the
application of Eq. 5.2 in comparison to Eq. 5.7 is given in Figure 5.6. For the dry
wood densities available, the use of Eq. 5.2 leads to underestimations of axial
thermal diffusivity (and hence sap flux density) of up to 10 %. Overall, based on a
modified Levene test to test for homogeneity of variance, the variability between
tree species is not more significant than the variability between trees of the same
species or even variability within the same tree according to height. Samples taken
at different heights can lead to large differences in calculated thermal diffusivity.
Figure 5.7 shows the thermal conductivities according to Eq. 5.2 and 5.7 for
different water contents of the European beech sample. Apparently, errors were
larger for lower and practically zero for higher water contents for this specific dry
wood density, which corresponds to the data presented in Figure 5.2. Overall, the
error for this specific sapwood sample was maximally 4.5 %.
X Data
0 0 0
m
ea
s 0.01
0.02
0.03
0.04 mc
mc_FSP
rb
X Data
0 0 0
0.01
0.02
0.03
0.04
Fibre saturation point MCFSP
0.00
0.01
0.02
0.03
0.04
MC
MCFSP
d
m
ea
s
0.00
0.01
0.02
0.03
0.04
(a) (b)
(c) (d)
0.15 0.25 0.35 0.15 0.25 0.35
Figure 5.5 Sensitivity measure δmeas for water content (MC), fibre saturation point (MCFSP
) and
dry wood density (ρd) for different MC
FSP and ρ
d 350 kg m-3 (a), 600 kg m-3 (b), 850 kg m-3 (c) and
1100 kg m-3 (d).
Interpreting MC in D determination
95
Tree Sampling
height
Sample
volume
(cm3)
MC(-) ρd
(kg.m-3)
Kax (Eq. 5.2)
(W.m-1.K-1)
Kax (Eq. 5.7)
(W.m-1.K-1)
EU1 BH 76 0.77 585 0.68 0.67
BH+50 53 0.79 567 0.67 0.66
EU2 BH 62 0.86 674 0.72 0.80
BH+50 68 0.91 653 0.72 0.79
EU3 BH 87 0.84 685 0.72 0.81
US1 BH 20 0.99 620 0.71 0.79
BH+50 90 0.99 586 0.70 0.74
US2 BH 122 0.66 723 0.72 0.76
BH+50 160 0.80 606 0.69 0.70
Table 5.2 Characteristics and calculated thermal conductivity Kax according to both Eq. 5.2
and 5.7 for the experimental trees. EU indicates European beech while US refers to American
beech. BH stands for Breast Height. For each sample, the corresponding stem diameter at
sample height, sample volume, water content (MC) and dry wood density (ρd) are given.
Chapter 5
96
EU1 EU2 EU3 US1 US2
Water content (kg
water kgdry wood-1)
0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
Th
erm
al co
nd
uctivity K
(W
m-1
K-1
)
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
Eq. 5.2
Eq. 5.7
Figure 5.6 Relative error in thermal diffusivity calculated as (Dax(Eq. 5.2)-D
ax(Eq.5.7))/D
ax(Eq.
5.7) for European and American beech. The striped bars indicate the lower sections (BH), while
the full bars are located 50 cm higher (BH+50).
Figure 5.7 Thermal conductivity (W m-1 K-1) calculated according to Eq. 5.2 and 5.7 for
different water contents for European beech with dry wood density 585 kg m-3.
Interpreting MC in D determination
97
When comparing the obtained sap flow using both Eq. 5.2 and Eq. 5.7 with the
gravimetric reference data for Eucalyptus caliginosa, it is clear that Eq. 5.7 leads to a
better fit (Figure 5.8) when applying the HR method, corrected for the relative radial
profile obtained with HFD. Linearly regressing the difference in results based on Eq.
5.2 and those based on Eq. 5.7 versus the gravimetric sap flux densities led to a
significant slope of 0.11. Hence, for this experiment, an underestimation of about 11
% for Dax was obtained when applying Eq. 5.2 instead of Eq. 5.7.
5.4 Discussion
As is clear from Figure 5.2, variations in water content, fibre saturation point as well
as dry wood densities amongst and within species, can lead to large over- or
underestimations of Kax. This results in a relative sap flux density error varying
between –15 and +22 %, dependent on ρd, MC and MC
FSP (Figure 5.3). For the lower
Gravimetric sap flux density (cm3 cm
-2 h
-1)
6 8 10 12 14 16 18 20 22
HR
sap
flu
x d
ensity (
cm
3 c
m-2
h-1
)
2
4
6
8
10
12
14
16
18
20
22
24
Eq. 5.2
Eq. 5.7
Figure 5.8 Sap flux density based on the Heat Ratio method with the diffusivity according to
Eq. 5.2 (black line) and Eq. 5.7 (grey line) for an Eucalyptus caliginosa tree (dry wood density
565 kg m-3 and water content 1.17) compared to the gravimetric reference. The dashed line is
the 1:1 line.
Chapter 5
98
dry wood densities (350 kg m-3), application of Eq. 5.2 leads to overestimation of
SFD, while for the upper values (1000 kg m-3) it leads to underestimation. For
average ρd (600 kg m-3) and MC of approximately 0.8, the error is negligible. Clearly,
the relative error is highly influenced by differences in ρd, which is confirmed in the
sensitivity analysis (Figure 5.4 and Figure 5.5). Notice that δmeas for MC is always
higher than for MCFSP
, even though for low dry wood densities the relative sensitivity
to MC approximates the relative sensitivity to MCFSP
for water contents between 0.7
and 1. Moreover, MCFSP
can be estimated according to Eq. 5.10, even though this is
only an empirical relationship and prone to slight over- or underestimations. As ρd is
known to be dependent not only on species but also on age, height and
environmental conditions, this parameter should be measured in close proximity of
the installed sap flow sensor. Likewise, differences in MC of 60 % and more have
been reported for different species (Peck, 1953). Moreover, MC poses a greater
challenge than ρd as it has been shown to also vary seasonally up to 25 % (Peck,
1953; Gibbs, 1958; Henderson & Choong, 1968) and even 40 % (Gibbs, 1958). More
recently, Borghetti et al. (1998) have shown a clear relationship between water
content in the xylem of twigs and twig water potential. As they have shown diurnal
patterns for twig water potential, these same patterns will occur for twig water
content, implying not only seasonally but also diurnal MC changes. Moreover, Scholz
et al. (2007) have detected daily changes of up to 18 % in relative water content,
calculated as the ratio of the differences between fresh and dry wood and saturated
and dry wood, for savanna species in Brazil. This implies that thoroughly accurate
measurements can only be made when the water content is known at the time of
measuring.
The results of the field experiment confirm the findings of the sensitivity analysis.
Clearly the difference between Eq. 5.2 and 5.7 is determined by both water content
and dry wood density (Figure 5.6). From Figure 5.7, one would expect that Eq. 5.2
overestimates for low water contents, but is quite accurate for higher water contents
of about 80 %. From Figure 5.6 and Table 5.2 however, it is clear that water content
alone is not sufficient to explain the over- or underestimations as for water contents
of about 80 %, large underestimations are obtained. These results also indicate that
within the same tree, differences in both water content and/or dry wood density can
occur, again stressing the importance of measuring both these parameters in
proximity of the sensor.
Interpreting MC in D determination
99
Figure 5.8 shows the possible impact of using Eq. 5 during field measurements of
sap flux density. Here, the relative difference in sap flux density due to this single
misinterpretation was about 11 %. When absolute measurements of sap flow are
needed, such differences can undoubtedly lead to erroneous results and
interpretations.
Up to now, Eq. 5.2 was considered applicable for sapwood without considering the
correct meaning of MC, hence missing the point of the original theory as developed
by Siau (1971). Unfortunately, in the papers mentioned in Table 5.1, no indications
are given of the dry wood density or water content used to calculate the thermal
diffusivity according to Eq. 5.2, making an estimation of the errors in sap flux
density for these studies impossible. However, for the model mentioned in
Wullschleger et al. (2011) where Kax is calculated according to Eq. 5.2 with a K
d value
for dry wood based on Jones et al. (2004), an error of about 15 % is made for an
assumed fibre saturation point of 0.3. Other heat transport models have probably
based the implementation of Kax on Eq. 5.2 as well.
Eq. 5.7 has the advantage of a correct underlying theory, although a slight
overestimation can be expected because of the simplification needed to apply the
empirical coefficients of Siau (1971) and the additional parameter MCFSP
needs to be
estimated. This parameter, however, can easily be estimated based on ρd (Eq. 5.10).
Moreover, Eq. 5.7 is not very sensitive towards MCFSP
, especially for high water
contents as is mostly the case for transpiring trees (Figure 5.4). Therefore, a wrong
estimation of this particular parameter will only lead to small errors in Dax
calculations according to Eq. 5.7. A much larger challenge lays in the determination
of the water content. While this parameter is measured at the moment of sampling,
the seasonal and daily variations are not taken into account. Taking multiple
samples during the season will improve accuracy, but is often practically difficult
due to enhanced tree damage. However, as the Tmax method has the prerequisite of
zero flow conditions and limitations of a single point measurement, Eq. 5.7 seems
to be the more favorable method for Dax determinations in the field as to our
knowledge, no other methods exist for determining thermal diffusivity during non-
zero flow conditions. Nevertheless, a combination of methods is desirable. For
instance, combining Time Domain Reflectometry (Wullschleger et al., 1996a; Nadler
et al., 2006) or tomography (Brazee et al., 2011; Bieker & Rust, 2012) estimates of
relative changes in water content with absolute measurements of Dax based on Eq.
Chapter 5
100
5.7 will likely result in improved sap flux density measurements but is of course
more labour and cost intensive. Another option is to apply the Compensation Heat
Pulse method as its operating principle is independent of Dax. Unfortunately, this
method is unable to resolve low or reverse flows.
5.5 Conclusions
Thermal diffusivity is a crucial parameter in modern sap flow calculation methods
such as the Heat Ratio method. However, due to a misinterpretation of MC in the
analytical equations, the current applied methodology to determine Dax can lead to
over- or underestimations of up to 10 % and more, depending on dry wood density,
water content and fibre saturation point when compared with the more accurate
approach which is presented in this chapter.
101
6 6 Development of the Sapflow+
method to measure sap flux
density and water content
After: Vandegehuchte, M.W. & Steppe, K. (2012). A triple-probe heat
pulse method for measurement of thermal diffusivity in trees. Agricultural
and Forest Meteorology, 160: 90-99.
Vandegehuchte, M.W. & Steppe, K. (2012). Sapflow+: a four
needle heat pulse sap flow sensor enabling non-empirical sap flux density and
water content measurements. New Phytologist, 196: 306-317.
BE2012/0030: Een methode voor het meten van sapstroom,
waterinhoud en thermische eigenschappen in planten
Chapter 6
102
Abstract
So far, no non-empirical method exists to measure reverse, low as well as high sap
flux densities independently of thermal diffusivity. Besides, existing sap flow
methods require multiple destructive wood core measurements to determine
temporal changes in sapwood water content, necessary to convert heat velocity to
sap flux density. In this chapter, a non-empirical heat pulse based method and
coupled sensor are presented which measure temperature changes around a linear
heater in both axial and tangential directions after application of a heat pulse. By
fitting the correct heat conduction-convection equation to the measured
temperature profiles, heat velocity and water content of the sapwood can be
determined. An identifiability analysis and validation tests on artificial and real
stem segments of European beech (Fagus sylvatica L.) confirm the applicability of
the method, leading to accurate determinations of heat velocity, water content and,
hence, sap flux density. The proposed method enables sap flux density
measurements across the entire natural occurring sap flux density range of woody
plants. Moreover, the water content during low flows can be determined, enabling a
correct conversion from heat velocity to sap flux density without multiple
destructive core measurements.
6.1 Introduction
As mentioned in previous Chapters, existing heat-based sap flow methods all have
their merits, but also suffer from specific limitations. The HFD method enables sap
flux density measurements at different depths in the sapwood and has the strength
of distinguishing high, low and reverse flows, but it remains empirical and can lead
to over- or underestimations depending on sap flux density, water content and
thermal characteristics of the wood (Chapter 3) (Vandegehuchte & Steppe, 2012b).
The TD method has suffered from these same limitations and is known to largely
underestimate sap flux density (Steppe et al., 2010).
For the heat pulse methods, the CHP method has the advantage that thermal
diffusivity does not need to be determined. However, it is incapable of determining
low and reverse flows (Becker, 1998; Green et al., 2009; Steppe et al., 2010). This was
partly resolved by Testi & Villalobos (2009) who used the CAG method, extending
measurement possibilities towards the lower sap flow range. This method, however,
The Sapflow+ method
103
necessitates an empirical calibration which is dependent on the thermal
characteristics of the sapwood. The HR method (Burgess et al., 2001a) can measure
both low and reverse flows but performs poorly at high flow rates (Burgess &
Dawson, 2008) and applies an inaccurate protocol to determine thermal diffusivity,
necessary as input parameter for the sap flux density calculations (Chapter 5). The
Tmax method (Cohen et al., 1981) determines thermal diffusivity correctly, but is
based on a zero flows and a single point analysis, making it susceptible to scatter.
Moreover, like the CHP method, it is unable to correctly estimate low and reverse
flows (Green et al., 2009). Besides, all heat pulse methods measure heat velocity
which needs to be converted to sap flux density based on water content of the
sapwood. To this end, wood cores are taken to estimate water contents. As taking
multiple wood cores increases wood damaging, temporal variations in water content
are usually not taken into account which may induce large errors in calculated sap
flux densities. While relative changes in stem water content can be estimated by
applications of methods such as Time or Frequency Domain Reflectometry,
resistivity tomography, gamma-ray attenuation and electrical resistance, these
methods require additional equipment, are difficult to interpret and struggle to take
the spatial variability of the sapwood into account (Wullschleger et al., 1996b;
Nadler & Tyree, 2008; Bieker & Rust, 2012). At present, sap flux density and stem
water content can be measured simultaneously by Magnetic Resonance Imaging (Van
As et al., 2009) but this laboratory technique is expensive, necessitates specific
tuning for different flow ranges and remains difficult to apply in the field despite
recent progress (Jones et al., 2012). While many methods have been developed to
determine sap flux density or stem water content separately, to our knowledge no
practically applicable method exists which combines both.
This Chapter describes how a new method and coupled sensor were developed,
further referred to as Sapflow+, building on the available knowledge within the sap
flow research community and combining the strengths of existing sap flow
methods. The Sapflow+ method is capable of non-destructively measuring high, low
and reverse sap flows, thermal wood properties and water content of the sapwood
based on thermodynamics. A theory based on earlier work of Kluitenberg & Ham
(2004) and the knowledge gained in Chapter 4 is presented to determine these
parameters based on conduction and convection of a short-duration heat pulse
away from an infinite line source in the sapwood. It is shown that by using this
Chapter 6
104
theory, sap flow, thermal wood properties and water content can be determined by a
four-needle probe. Results of both Finite Element Modelling and lab experiments are
presented which demonstrate the applicability of the theory for measuring sap flux
density and water content of fresh sapwood.
6.2 Materials and methods
6.2.1 Theory
The theory applied is developed for an infinitely long linear heater of zero radius in
an infinitely large medium. Based on the work of Kluitenberg & Ham (2004) and
Vandegehuchte & Steppe (2012c), the temperature distribution in an anisotropic
media is expressed as (see also Chapter 4):
1
0
( )² ²exp
44
t
h
ax tgax tg
x V tq c yT t dt
t K KK K
for 0<t<=t0 (6.1)
0
1 ( )² ²exp
44
t
h
ax tgt tax tg
x V tq c yT t dt
t K KK K
for t
0<t (6.2)
with ∆T the temperature difference (K) between the measured temperature at time t
(s) after application of the pulse and the measured temperature before the heat
pulse, measured at a distance x (m) axial and y (m) tangential from the heater,
respectively. Kax is the axial and K
tg the tangential thermal conductivity (W m-1 K-1), ρ
the density (kg m-3) of the sapwood, c the specific heat capacity of the sapwood
(J kg-1 K-1) and q the energy input per unit length of the heater per unit time (W m-1).
By measuring the temperature change ∆T at three different positions around the
heater needle, a multi-parameter model which solves Eq. 6.1 and 6.2 for each
position can be fitted to retrieve the parameters of interest, namely Kax, K
tg, ρc (the
volumetric heat capacity, J m-3 K-1) and Vh. In this model, a temperature correction
for changing sapwood temperatures independent of the heat pulses is applied. By
determining the temperatures before and after the heat pulse, the slope of
temperature change is calculated which is then subtracted from the modelled
temperature changes.
This multi-parameter model was implemented, simulated and calibrated using the
plant modelling software PhytoSim (Phyto-IT BVBA, Mariakerke, Belgium). For model
The Sapflow+ method
105
calibration the simplex method, originally developed by Nelder & Mead (1965), was
used to minimize the weighted sum of squared errors between measured and
simulated values of the temperatures. The weighted sum of squared errors objective
value for each fit to the axial and tangential temperature data indicates the
goodness of fit:
1 1
1 1( )²
²
k n
ij ij
i j
WSSE m yn
(6.3)
where WSSE is the weighted sum of squared errors objective, k the number of
objective variables (3, for each position at which the temperature is measured), σ²
the measurement error variance for objective variable i (for the three temperature
measurements a value of 0.02 for σ was applied, based on the calibration of the
thermocouples in a warm water bath), n the number of measurement points for
objective variable i, mij the jth measurement value of objective variable i and y
ij the
corresponding simulation value.
6.2.2 Water content
If the volumetric heat capacity (ρc, J m-3 K-1) of the sapwood is known, its water
content (MC, kg water per kg dry weight) can directly be determined (Swanson,
1983):
1dw
w d
cMC c
c
(6.4)
with cw and c
dw the heat capacity of water (4186 J kg-1 K-1, Martin & Lang (1933)) and
dry wood (1200 J kg-1 K-1, Edwards & Warwick (1984)), respectively and ρd the dry
wood density (kg m-3), which can be measured once by sampling a wood core.
6.2.3 Sensor design
To apply the theory, a needle probe was designed consisting of a linear heater and
three measurement needles located at specific distances, respectively, axially
upstream, downstream and tangentially from the heater (Figure 6.1). The three
stainless steel measurement needles have a length of 35 mm and a diameter of 1.1
mm. In each measurement needle a copper-constantan thermocouple is located at
20 mm from the needle basis. Notice that, similar as for the HR method,
thermocouples could be installed at different depths to assess radial differences in
Chapter 6
106
sap flux density. This, however, requires additional logging capacity. Due to
practical limitations, it was in this set-up not possible to install more than one
thermocouple in each measurement needle.
The heater needle has a length of 38 mm and a diameter of 1.1 mm. The heater is
slightly longer than the measurement needles to avoid side effects at the end of the
sensor, similarly as for the HFD method. An enameled resistance wire with a known
resistance (0.02341 Ω mm-1) is coiled around this heater. Heat pulses of 6 seconds
were generated by applying 5 V to the heater. The theoretical amount of heat
released by this heater, q (W m-1), was calculated similarly as done by Campbell et al.
(1991):
2
'RR
s
s
Uq (6.5)
with U (V) the applied voltage, Rs (Ω) the resistance of the heater and R
s’ (Ω m-1) the
resistance of the heater per unit length.
Figure 6.1 (a) Schematic of a tangential section of the stem xylem with arrangements of the
thermocouples around the heater of the Sapflow+ sensor; and (b) Schematic of the Sapflow
sensor installed in the sapwood (SW) of a stem.
The Sapflow+ method
107
A CR1000 datalogger (Campbell Scientific, Loughborough, UK) was used to control
the heat pulse, monitor the applied voltage and measure the temperatures as a
function of time.
6.2.4 Identifiability analysis
Application of the Sapflow+ model will only be successful when the parameters on
which the model is calibrated, are identifiable. Therefore, an identifiability analysis,
consisting of a sensitivity and a correlation analysis, was conducted for the model
parameters ρc, Kax, K
tg and V
h. Indeed, a model parameter is said to be identifiable if
it has sufficient influence on the model outputs, in this case the changes in
temperature before and after the pulse at three positions around the heater, ∆T1,
∆T2 and ∆T
3 (high sensitivity) and at the same time is not correlated with other
model parameters (no linear dependencies with other model parameters) (De Pauw
et al., 2008).
To examine the first condition of parametrical identifiability, a sensitivity measure
δmeas similar to that of Brun et al. (2002), Steppe et al. (2006) and De Pauw et al.
(2008) was used. This measure is an indication of the relative importance of the
different parameters for the model output. The centralized relative sensitivity
function of model variable yi towards parameter θ was calculated as (see also Section
5.2.1):
( ) ( )( )
2 ( )
i ii
i
y yS y
y
(6.6)
with ∆θ taken as 1 % of the source component value θ.
The sensitivity measure δmeas was then calculated as:
cmeasS
n (6.7)
with Sc the vector constructed by concatenating the sensitivity function vectors of
T1, T
2 and T
3, and n the total number of measurement instances (summed overall
measured variables) which allows accounting for measurement quantities. ||Sc||
corresponds to the norm of Sc which is the square root of the sum of squared values
of each of the vector elements.
Chapter 6
108
To assess correlations between the model parameters, a collinearity analysis was
performed (Brun et al., 2002; Steppe et al., 2006) which allows detection of
dependencies between the model parameters. To this end, the collinearity index γ
was calculated based on the minimum eigenvalue of STS with S the normalized
sensitivity matrix composed of columns:
1 c
Tc
S
S
min
= , SS S
(6.8)
This collinearity index ranges between unity, if the sensitivity functions are
orthogonal, and infinity for an exact linear dependency between the sensitivity
functions. The threshold was put at 15 following Brun et al. (2002). Indices below 15
point to weak dependencies, whereas indices above 15 are associated with moderate
to strong relations. These indices can be calculated for all model parameters or on a
subset of specifically selected parameters.
The quality of the estimated parameters was further checked based on the
parameter estimation error covariance matrix. From this matrix, the standard errors
of the parameters can be calculated as σ(θi)=√V
ii with V
ii an element of the diagonal
of the covariance matrix. Sensor verification
A 3D Finite Element Model (FEM) was implemented to compare the theoretical Eq.
6.1 and 6.2, developed for a perfect heater (infinite length and zero radius) in an
infinitely large environment, with a more realistic situation. To this end, a cube of
immobilized water with length 10 cm was modelled. In this cube, the three sensor
needles and heater were located with their according dimensions, similarly as in
Section 3.3. While for the HDF model a continuous heat input was applied, here a
heat pulse of 160 W m-1 was implemented.
These modelling results were then compared with actual measurements in water
immobilized with 2 g agar l-1 (Campbell et al., 1991; Ren et al., 2003). The small
amount of agar was added to prevent natural convection in the water and is
assumed to have a negligible effect on the thermal characteristics. This immobilized
water has the advantage that it is in direct contact with the heater and needles.
From the known thermal properties of this medium, the heat input q as calculated
according to Campell et al. (1991) can then be checked for each sensor and a
correction factor calculated if necessary.
The Sapflow+ method
109
6.2.5 Comparison of heat pulse methods
Next to immobilized water, moist wood was modelled according to the same
principles and with the same dimensions as for the immobilized water. The wood
was considered as an anisotropic medium in which unidirectional convection
occurred. For this wood, a dry wood density of 550 kg m-3 was applied, with varying
water contents and accordingly varying specific heat capacity and thermal
conductivity (Vandegehuchte & Steppe, 2012a). In this wood, sap flux densities
ranging from -15 (reverse flow) to 100 cm3 cm-2 h-1 (high flow) were modelled. For
this model the CHP, HR, Tmax and Sapflow+ method were compared for 6 s heat
pulses of 160 W m-1. For the Tmax method, formulas for a non-ideal heat pulse as
mentioned in Kluitenberg & Ham (2004) adapted for anisotropic wood were applied
(Eq. 2.8, 2.9) (Vandegehuchte & Steppe, 2012c), while for the CHP (Eq. 2.5) and the
HR (Eq. 2.10) the original equations valid for an ideal heat pulse were applied
(Swanson & Whitfield, 1981; Burgess et al., 2001a). Notice that in these equations as
mentioned in Section 2.3, D really is the axial diffusivity Dax, as explained in Chapter
4.
Both for the HR and the CHP method, the original equations are theoretically not
applicable for non-ideal pulses. For the HR method, however, it is mentioned in
Burgess et al. (2001a) that there was no significant difference when applying heat
pulses of 6 seconds compared to shorter pulses. This was also confirmed by
comparing the theoretical results of applying the original HR equation to the
temperatures as modelled by Eq. 6.1 and 6.2 for heat pulses ranging between 1 and
10 seconds. As no significant difference between these results was obtained, the
original HR equation was deemed valid for pulses of 6 seconds. For the CHP
method, on the other hand, an underestimation of 15 % was noticed when
theoretically applying the ideal heat pulse equation for non-ideal heat pulses of 6 s.
This underestimation needs to be taken into account when interpreting the results.
As all methods are based on the insertion of needles in the wood, distinction was
made between wood without and with wound effects, the latter modelled as regions
surrounding the sensor needles in which zero flow occurs with a width of 1.5 mm
and a length stretching from 0.2 mm below the lower to 0.2 mm above the upper
needle. This wound effect simulates the interruption of flow due to the invasiveness
of the needles and will lead to a diversion from the ideal condition on which all
Chapter 6
110
mentioned methods are based, namely a uniform flow distribution in the wood. This
leads to underestimations in the calculated heat velocities. Based on the modelling
results, however, a correction can be developed to take these wound effects into
account (Swanson & Whitfield, 1981).
6.2.6 Measurements of sap flux density in artificial sapwood
The Sapflow+ method was tested on an artificial stem segment, consisting of a
plastic cylinder filled with fine sawdust of European beech (Fagus sylvatica L.). This
artificial segment has the advantage of a radial homogenous sap flux density profile
and, given the high porosity, allowed a wide range of sap flux densities to be
applied. The segment was installed in a verification system as proposed by Steppe et
al. (2010) (Figure 6.2). Flow rates of water were held constant by maintaining a
constant head of water pressure on the segment using the Mariotte’s bottle principle
(McCarthy, 1934). A closed water-filled 5-L Erlenmeyer flask was equipped with two
glass tubes located at the same depth in the flask: one tube functioned as an air
inlet, while the other, connected to a third glass tube via flexible tubing, functioned
as a siphon. By adjusting the height of the flask (and thus the bottom of the air
inlet), the water-filled siphon delivered the flow of water required to maintain a
constant head (h = distance between the bottom of the air inlet and the surface of
the segment) on the segment, regardless of the changing water level within the
flask. Water passing through the segments was continuously measured using an
electronic balance (PS 4500/C1, Henk Maas weegschalen BV, 4264 AW Veen, the
Netherlands).
The Sapflow+ method
111
At the end of the measurements, the volume of the sawdust column was determined
and the sawdust was dried and weighed to determine the dry wood density. As high
flows for this artificial column were expected, a needle configuration of (10,0); (-5,0)
and (0,5) mm was applied for the axial downstream, axial upstream and tangential
needle, respectively, enabling comparison with the CHP method.
6.2.7 Measurements of sap flux density in sapwood
Next to the artificial segment, the method was also tested in sapwood of European
beech (Fagus sylvatica L.). To this end, two trees of approximately 15-years old with
a diameter at breast height of about 12 cm were cut at the experimental forest
‘Aelmoeseneie’ of Ghent University (Gontrode, Belgium). The cut ends were sealed
with parafilm (Parafilm M, SPI supplies/Structure Probe Inc., West Chester, PA
19380, USA) and enclosed in plastic bags to minimize evaporation. The stems were
Figure 6.2 Schematic diagram of the Mariotte-based verification system (from Steppe et al.
(2010)) used for testing the accuracy of the Sapflow+ method.
Chapter 6
112
then transported to the Laboratory of Plant Ecology, Ghent University, and cut into
segments of approximately 20 cm length.
Before installing the cut stem segments in the experimental set up, cut surfaces
were wetted and trimmed using a razor blade to re-open possibly closed vessels
(this was visually confirmed using a stereomicroscope). A 2-cm strip of bark at the
top end of the segment was removed to ensure that water only passed through the
stem xylem. On these segments, a 30-cm high plastic cylinder was fixed directly to
the xylem using silicone and double-sticking adhesive tape. After a drying phase of
~18 hours for the silicone to harden, the Sapflow+ sensor was installed. Accurate
vertical spacing and parallel drilling was achieved by using a drill-bit template.
Notice that before installing the sensors, the bark was removed to ensure that the
heater was completely located in the sapwood.
At the end of the experiment, a small disc of the segment was cut from which
volume, moist weight and dry weight after drying 24 h in a 50°C oven were
determined. From these values, water content and dry wood density were calculated.
Besides, the segment was cut through at the needle position to accurately determine
the exact spacing between the measurement needles and to measure the wound
width. As lower flows were expected in comparison with the artificial column, it was
preferred to compare the Sapflow+ results with the HR method. As it was noticed
that for distances of 10 mm, the axial downstream signal was rather low which
reduces the sensitivity of the HR method, a smaller distance of 7.5 mm was chosen,
resulting in a needle configuration of approximately (7.5,0); (-7.5,0) and (0,7.5) mm
for the axial downstream, axial upstream and tangential needle, respectively.
Following equation for the HR method was applied (Burgess et al., 2001a):
2 24 ln( / )
2 ( )
ax down up down up
h
up down
D t T T x xV
t x x (6.9)
with Dax the thermal diffusivity (m2 s-1), ∆T
down and ∆T
up the downstream and
upstream temperature differences, respectively, at time t after application of the
pulse and xdown
and xup
the exact axial downstream and upstream distances of the
measurement needles to the heater, respectively. Unlike the original HR equation
(Eq. 2.10), Eq. 6.9 takes into account differences in the upflow and downflow needle
distance. Thermal diffusivity was determined according to Cohen et al. (1981) as it
has been shown that the original method to determine Dax presented in Burgess et
The Sapflow+ method
113
al. (2001a) was incorrect (Vandegehuchte & Steppe, 2012a). Table 6.1 summarizes
the applied materials, methods and objectives of this Chapter.
Material Method Objective
Immobilized
water
Finite Element Modelling Investigation of influence of
theoretical assumptions leading to
Eq. 6.1 & 6.2
Immobilized water
(2 g agar L-1)
Confirmation of modelling results
Wood Finite Element Modelling Estimation of wound effects
Comparison of heat pulse methods
Artificial column with
sawdust
Gravitational validation of Sapflow+
Comparison with CHP method
Fagus sylvatica segments Gravitational validation of Sapflow+
Comparison with HR method
6.3 Results
6.3.1 Identifiability analysis
Figure 6.3a, b and c show the relative sensitivity functions for the ∆T signals,
respectively at position (10 mm, 0 mm), (-5 mm, 0 mm) and (0 mm, 5 mm) from the
heater needle. The sensitivity functions of the parameters are clearly different for
the different measurement positions. For instance, a positive Vh will have a negative
relative sensitivity for positions upstream and tangentially from the heater, while
the relative sensitivity will be (partly) positive for downstream positions. Kax,
however, will have a positive relative sensitivity for axial positions, but negative for
Table 6.1 Summary of the applied materials, methods and objectives.
Chapter 6
114
the tangential position and vice versa for Ktg. Figure 6.3d gives an indication of the
overall sensitivity of the parameters for different heat velocities. It should be noted
that, for zero flow, the sensitivity measure for Vh is much lower than for the other
parameters (not visible in Figure 6.3d). A 1 % change in Vh will hardly influence the
∆T signals if Vh is much lower than for the other parameters (not visible in Figure
6.3d). A 1 % change in Vh will hardly influence the ∆T signals if V
h is approximately
zero. Nevertheless, the model remains practically applicable as an error of 1 % in the
Vh determination for such a low value is negligible and, for higher absolute V
h
values, the sensitivity increases rapidly. Moreover, as the collinearity index remained
below 8.5 across the complete natural range of water contents and sap flux
densities (from -15 to 110 cm3 cm2 h-1 (Vertessy et al., 1997; Burgess & Bleby, 2006;
Cohen et al., 2008)), the model can be considered to be identifiable if the heat input
and measurement positions are known.
Rela
tive s
en
sitiv
ity
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
Time (s)
0 50 100 150 200
Rela
tive s
en
sitiv
ity
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
Vh (cm h-1)
-10 0 40 120
Se
nsitiv
ity m
ea
sure
(m
eas)
0.000
0.002
0.004
0.006
0.008
0.010
Vh -10 cm3 cm
-2 h
-1
Vh 40 cm3 cm
-2 h
-1
Time (s)
0 50 100 150 200
Rela
tive s
en
sitiv
ity
-0.010
-0.005
0.000
0.005
0.010
Vh
C
Kax
Ktg
Kax
Ktg
Vh
c
(a) (b)
(c) (d)
Figure 6.3 Relative sensitivity functions for Vh (-10 cm3 cm-2 h-1: black, 40 cm3 cm2 h-1: grey), ρc
(2.4×106 J m-3 K-1), Kax (0.62 W m-1 K-1) and K
tg (0.42 W m-1 K-1) for position (10 mm, 0 mm) (a), (-
5 mm, 0 mm) (b) and (0 mm, 5 mm) (c) with reference to the heater. The sensitivity measures
for all parameters are given in (d) for different heat velocities.
The Sapflow+ method
115
6.3.2 Sensor verification and calibration
Figure 6.4a shows the temperatures as obtained with FEM for a distance of 7.5 mm
from the heater in immobilized water. As this medium is isotropic, exactly the same
results are obtained whether the measurement needle is located axially or
tangentially from the heater. Compared to the theoretical Eq. 6.1 and 6.2, there is
only a small difference in temperatures obtained by FEM (Figure 6.4a). The small
differences are probably a result of the fact that in the latter, actual needles are
implemented with finite boundaries of a specific material, i.e. stainless steel. When
applying Sapflow+ to the FEM data, following values are obtained (relative difference
with the actual values is indicated between brackets): ρc: 4.108×106 J m-3 K-1 (-1.8 %),
Kax, K
tg: 0.6176 W m-1 K-1 (+1.2 %) and V
h: 0 m3 m-2 s-1.
In Figure 6.4b, actual measurements with the Sapflow+ sensor in immobilized water
are given. As, for the three measurement needles at (0,7.5), (7.5,0) and (-7.5,0) mm
from the heater, similar temperatures were obtained, the data are only plotted for
one needle. When comparing these measurements with Eq. 6.1 and 6.2, the theory
seems to overestimate the temperature. If, however, the heat input q, as calculated
Time (s)
0 50 100 150 200
Te
mpe
ratu
re (
°C)
19.9
20.0
20.1
20.2
20.3
20.4
20.5
FEM
Theoretical Eq. 6.1 and 6.2
Curve fitting for FEM
Time (s)
0 50 100 150 200 250
Te
mpe
ratu
re (°C
)
24.4
24.5
24.6
24.7
24.8
24.9
25.0
Theoretical Eq. 6.1 and 6.2
Curve fitting for 0.84*q
Measured temperatures
(a) (b)
Figure 6.4 (a) Temperature data at 7.5 mm from the heater for the Finite Element Model
(FEM) of immobilized water compared with the theoretical Eq. 6.1 and 6.2 for the thermal
properties of water (ρc=4.186×106 J m-3 K-1, Kax=K
tg=0.61 W m-1 K-1, V
h=0 m3 m-2 s-1) and the
application of Sapflow+ to the FEM data; (b) Measured temperatures with the Sapflow+ sensor
in immobilized water compared to the fitted temperatures for the q calculated according to
Campbell et al. (1991) and after calibration for q, leading to an optimal value of 0.84×q. For
both the FEM as the actual measurements, a heat pulse of 6 s and 160 W m-1 was applied.
Chapter 6
116
according to Campell et al. (1991) is reduced, a good fit is obtained (objective value
of 13.17 compared to 12 for an ideal fit).
Figure 6.5 stresses the importance of temperature correction. During the
measurement, the ambient conditions generally change during the day, influencing
the measured temperature peaks (Figure 6.5a). Without temperature correction,
application of the presented method would lead to erroneous results. Figure 6.5b
shows the curve fitting without calibration for the known thermal parameters of
stabilized water when no temperature correction is applied. When calibrating the
parameters of Eq. 6.1 and 6.2 to obtain a good fit, erroneous results are obtained
(ρc=4.344×106 J m-3 K-1 (+4 %), Kax=K
tg=0.824 W m-1 K-1 (+34 %)) and the fit only has an
objective value of 694 compared to a 2.54 for an ideal fit. If, however, a temperature
correction is applied, the method is again able to correctly determine the desired
variables from the curve fitting procedure. The data further shown, have been
corrected for temperature effects.
Time (h)
0 2 4 6 8 10 12 14 16 18 20
Te
mp
era
ture
(°C
)
23.8
24.0
24.2
24.4
24.6
24.8
25.0
25.2
Water temperature at (7.5,0)
Air temperature
Time (min)
484 486 488 490 492
Te
mp
era
ture
(°C)
24.3
24.4
24.5
24.6
24.7
24.8
24.9Measurement
Corrected fit
Uncorrected fit
Uncorrected fit, calibrated
(a) (b)
Figure 6.5 (a) Measured air temperature and temperature in immobilized water at location
(7.5,0) mm from the heater for heat pulses of 6 s and 105 W m-1, applied every 45 min; and (b)
Measured water temperature for one heat pulse compared to the curve fit for ρc=4. 186×106 J
m-3 K-1 and Kax=K
tg=0.61 W m-1 K-1 with and without temperature correction. When calibrating
the fitted curve without temperature correction, values of 4.344×106 J m-3 s-1 (+4 %) for ρc,
0.824 W m-1 K-1 (+34 %) for Kax and for K
tg and 0 m3 m-2 s-1 for V
h are obtained.
The Sapflow+ method
117
6.3.3 Comparison of heat pulse methods by FEM
In Figure 6.6a the calculated heat velocities according to the Sapflow+, Tmax, CHP
and HR method are given for FEM of sapwood without wound effects. Similar results
were obtained for other water contents and dry wood densities. Figure 6.7 shows
that, for HR measurements at high heat velocities, the upstream ∆T signal is nearly
zero while the downstream ∆T signal is lower than for lower heat velocities between
60 and 100 s, the time period for calculating the average ∆Tdown
/∆Tup
signal.
-20 0 20 40 60 80 100 120 140
Fit SapFlow+
Vh FEM (cm h-1)
-20 0 20 40 60 80 100 120 140
Vh
sensor
(cm
h-1
)
-50
0
50
100
150
200
HR
SapFlow+
Tmax
CHP
SapFlow+
HR
Tmax & CHP
y=0.622x
R2=0.995(a) (b)
Figure 6.6 Heat velocity calculated according to the Heat Ratio (HR), Tmax, Compensation
Heat Pulse (CHP) and Sapflow+ method based on the temperature data obtained by FEM for
sapwood with a dry wood density of 550 kg m-3 and a water content of 0.75 without (a) and
with (b) wound effect. The heat velocity range for which each method is applicable is
indicated. The full line indicates the 1:1 line.
Chapter 6
118
In addition to accurately determining heat velocity, Table 6.2 indicates that the
Sapflow+ method is also capable of estimating the water content of the sapwood, a
crucial parameter for the conversion of heat velocity to sap flux density. Moreover,
the thermal conductivities of the sapwood are estimated as well, although less
accurately as the method is less sensitive towards these parameters.
MC FEM MC SF+ Kax FEM K
ax SF+ K
tg FEM K
tg SF+
0.748 0.748 (±0.013) 0.6275 0.607 (±0.014) 0.42 0.46 (±0.0230)
0.855 0.861 (±0.007) 0.6634 0.637 (±0.030) 0.44 0.467 (±0.022)
0.955 0.921 (±0.016) 0.6964 0.663 (±0.028) 0.46 0.467 (±0.018)
1.045 1.04 (±0.007) 0.7263 0.687 (±0.048) 0.48 0.511 (±0.027)
Time (s)
0 20 40 60 80 100 120
C
)
-1
0
1
2
3
4
5
6
Tup_Vh100
Tdown_Vh100
Tup_Vh110
Tdown_Vh110
Figure 6.7 The ∆Tup
and ∆Tdown
HR signal for a heat velocity of 100 and 110 cm h-1. While for
the ∆Tup
signal the difference for both flows is hardly noticeable, the ∆Tdown
signal between 60
and 100 s is clearly higher for Vh 100 cm h-1.
Table 6.2 Water content (MC), axial and tangential conductivity (Kax, K
tg) implemented in the
Finite Element sapwood model (FEM) and the corresponding average values for heat velocities
from -20 to 140 cm3 cm-2 h-1 calculated with the Sapflow+ method (SF+). Standard deviations
are given between brackets.
The Sapflow+ method
119
In practice, however, sap flux density measurements are influenced by wound
effects. Figure 6.6b shows the modelling results when wound effects are introduced,
which more closely correspond to reality in comparison with Figure 6.6a. Clearly all
methods are affected. When fitting a linear regression, the Sapflow+ method led to
the best fit and highest slope, although the R2 value did not differ much compared
to the other methods (Table 6.3). When regressing the difference between the
Sapflow+ results and the results of the other methods, slopes were all significantly
different from zero indicating a significant difference between the Sapflow+ and the
other methods. For both the CHP and Tmax method, the intercept is also
significantly different from zero. Moreover, the R2 value for the regressed difference
between Sapflow+ and HR method is only 0.566 because of the inaccurate HR
results at high heat velocities (Table 6.3). The main difference, however, lays in the
applicability of the methods across the sap flow range. Based on these modeling
results, the Sapflow+ method is the only method leading to good results for
negative, low a well as high heat velocities. Hence, by applying a simple linear
wound correction (as can be seen in Figure 6.6b), accurate heat velocities across the
entire range of sap flux densities can be determined by this method. The wound
effect, however, also influences the calculated thermal parameters and hence water
content (Figure 6.8). For low heat velocities ranging between -15 and 45 cm h-1, the
thermal parameters and water content are determined quite accurately (relative
error <5 %). For larger absolute heat velocities, however, the relative errors increase
and become more dependent on the water content. Based on the modelling results,
however, a non-linear correction can be applied based on the pooled data for all
water contents which will reduce the error to a maximum of 7 %.
SF+ HR Tmax CHP SF+-HR SF+-Tmax SF+-CHP
Slope 0.62* 0.56* 0.48* 0.31* 0.057* 0.100* 0.294*
Intercept 1.56 3.18 0.40 8.47* -1.62 4.857* -4.847*
R2 0.997 0.979 0.994 0.981 0.567 0.871 0.995
Table 6.3 Linear regression results of the different heat pulse methods resulting from the
Finite Element sapwood model (FEM) with wound effects. Results were regressed against the
implemented heat velocity Vh. Significant results are indicated by *.
Chapter 6
120
6.3.4 Measurements on artificial sapwood
Figure 6.9a shows the heat velocity calculated according to the Sapflow+ and the
CHP method in comparison with the gravimetric heat velocity for the artificial
column. As no direct measurement of MC was possible on the artificial column, the
value determined by the Sapflow+ method for zero flow was applied for all
measurements, given the negligible error for MC determination during zero flow in
the modelling results. This value was also applied to calculate gravimetric heat
velocity from the measured gravimetric sap flux density. In Figure 6.9b, the relative
error in MC determined by Sapflow+, with the MC at zero flow determined by
Sapflow+ taken as reference, is given. Again, the error increases with increasing heat
velocity because of the interruption of flow around the needles (wound effect).
Vh
(cm h-1
)
0 50 100 150
Rela
tive
err
or
in M
C (
%)
-10
0
10
20
30
40
MC 75
MC 85
MC 95
MC 105
y=1.57-0.17x+0.0063x2-2.5*10
-5x
3
R2=0.98
Figure 6.8 Relative error (%) of water content calculated as the difference in water content
determined by the Sapflow+ method and the model input water content divided by the model
input water content, for different water contents and heat velocities.
The Sapflow+ method
121
6.3.5 Measurements on sapwood
For real sapwood segments of European beech (Fagus sylvatica L.), a maximal heat
velocity (derived from the sap flux density, dry wood density and water content of
the sapwood according to Eq. 2.4) of 45 cm h-1 was obtained (Figure 6.10a).
Regressing the Sapflow+ and HR results to the heat velocity led to a slope of 0.61
and R2 of 0.982 for the HR method, and 0.61 and 0.978, respectively, for Sapflow+.
Given an average wound width of 1.51 mm, the obtained slopes are in agreement
with the modeling results. Clearly, for heat velocities up to 45 cm h-1, the HR and
Sapflow+ method perform equally. This was confirmed by linearly regressing the
difference in the Sapflow+ and HR method results to the gravimetric heat velocity,
which did not lead to a significant slope (p=0.824) or intercept (p=0.697) (Figure
6.11). Nevertheless, differences between stem segments can be noted (Table 6.4). It
should be noted that, for both methods, measurements were only performed at a
single sapwood depth. While the relative error in calculated water content was on
average 0.8±1.4 % for zero flow conditions, it increased to 10 % for higher heat
velocities (Figure 6.10b).
Vh gravimetric (cm h-1)
0 50 100 150 200
Vh S
ap
Flo
w+
(cm
h-1
)
-50
0
50
100
150
200
250
SapFlow+
CHP
y=0.79x
R2=0.99
y=0.62x
R2=0.99
0 20 40 60 80 100 120 140 160
Re
lativ
e e
rror in
MC
(%)0
5
10
15
20
25
30
35
(a) (b)
Figure 6.9 (a) Heat velocity (Vh) in the artificial column calculated by Sapflow+ and the
Compensation Heat pulse method (CHP) in comparison to the gravimetric heat velocity
(determined from gravimetric sap flux density based on the water content calculated by
Sapflow+ for zero flow). The broken line indicates the 1:1 line; and (b) Relative error in water
content (MC) determination by Sapflow+ with the zero flow measurement as reference value.
Chapter 6
122
Vh gravimetric (cm h-1)
0 10 20 30 40 50
Vh S
ap
flo
w+
(cm
h-1
)
-5
0
5
10
15
20
25
30
S1
S2
S3
S4
S5
y=0.5844x
R2=0.97
0 10 20 30 40 50
Re
lativ
e e
rror in
MC
(%)
-6
-4
-2
0
2
4
6
8
10
12
(a) (b)
Vh calculated by Sapflow+(cm h
-1)
0 5 10 15 20 25
Vh c
alc
ula
ted
by H
R (
cm
h-1
)
0
5
10
15
20
25
y=0.99x
R2=0.94
Figure 6.10 (a) Heat velocity (Vh) in the stem segments calculated by Sapflow+ in comparison
to the gravimetric heat velocity; and (b) Relative error in water content determination by the
Sapflow+ method with the gravimetrically determined water content as reference value. For
the 5 segments, an average wound width of 1.51 mm was measured.
Figure 6.11 Heat velocity (Vh) calculated by the Heat Ratio method (HR) versus heat velocity
calculated by the Sapflow+ method for all sapwood segments. The full line indicates the 1:1
line.
The Sapflow+ method
123
S1 S2 S3 S4 S5
Slope 0.46* 0.55* 0.68* 0.82* 0.60*
Intercept 1.1* 0.97 0.40 -0.73 0.29
R2 0.995 0.980 0.976 0.994 0.953
6.4 Discussion
6.4.1 Applicability of the Sapflow+ method
From the identifiability analysis, the model is theoretically able to correctly
determine Vh, ρc, K
ax and K
tg across the entire natural range of sapwood water
contents and sap flux densities. This was also confirmed by the results of FEM
(Figure 6.4a). For the measurements in stabilized water, the fit was not as accurate
as for FEM, unless the heat input was reduced in the Sapflow+ model (Figure 6.4b).
As the heater needles are manufactured manually, the heater wire is not entirely
inserted in the wood to facilitate coupling to the voltage source. Moreover, it is
likely that some of the generated heat is taken up by the heater material itself and
hence not given off to the surrounding wood. Therefore, a calibration procedure is
necessary to correct the parameter q for every sensor. As q is only dependent on the
heater needle itself and not on the thermal characteristics of the sapwood, this
sensor-specific correction should be applicable for all further measurements.
To determine q correctly, it can be incorporated in the model calibration. If the
quotient of the volumetric heat capacity ρc and the heat input q is again considered
as a single parameter q/ρc, this parameter can be estimated along with Vh, D
ax and
Dtg by applying a curve fitting procedure on following equations:
1
0
( )²1 ²exp
44
t
h
ax tgax tg
x V tq yT t dt
t D Dc D D
for 0 < t <= t0 (6.10)
Table 6.4 Linear regression results for the Sapflow+ method applied for the different stem
segments as shown in Figure 6.10. Significant results are indicated by *.
Chapter 6
124
0
1 ( )²1 ²exp
44
t
h
ax tgt tax tg
x V tq yT t dt
t D Dc D D
for t
0 < t (6.11)
Identifiability analysis shows that this curve fitting leads to accurate estimations of
q/ρc for low and average heat velocities (up to 50 cm h-1) but the procedure is no
longer identifiable for higher heat velocities. As a single wood core needs to be
taken anyhow to determine the dry wood density, also the MC of this wood core can
be determined by weighing its initial wet weight and its dry weight after drying. This
way, ρc can be determined:
d w dwc c MC c (6.12)
As ρc is now known at the moment of wood core sampling and q/ρc can
simultaneously be determined from the model fitting, the correct q can be assessed
and further applied in the measurements according to Eq. 6.1 and 6.2. This way, an
in-situ calibration is obtained which is more practical than the calibration procedure
based on measurements in stabilized water.
In addition to a correct heat input, precise positioning of the sensor needles needs
to be known to obtain good results, which was also mentioned by Swanson (1983),
Jones et al. (1988) and later by Kluitenberg et al. (1995) for other heat pulse based
methods. A 5 % error in needle spacing can lead to up to 16 % error in calculated
heat velocities and MC, with the error depending on the heat velocity and relatively
larger for lower flows (Table 6.5).
Similar error percentages were obtained for other MC values. It is thus
recommended to use a template to install the needles in the sapwood. In addition, a
fixed sensor design can aid users to avoid spacing errors.
125
xdown
1 0.95 1.05 1 1 1 1 0.95 1.05 0.95 1.05 0.95 1.05 0.95 1 1.05 1.05 0.95 1 1 0.95 0.95 0.95 1.05 1.05 1.05
xup
1 1 1 1.05 0.95 1 1 0.95 1.05 1.05 0.95 0.95 1.05 1 0.95 1 1 1 0.95 1.05 0.95 1.05 1.05 1.05 0.95 0.95
ytg 1 1 1 1 1 0.95 1.05 1 1 1 1 0.95 1.05 0.95 0.95 1.05 0.95 1.05 1.05 0.95 1.05 1.05 0.95 0.95 0.95 1.05
Vh 50 35 0.95 1.05 1.00 1.00 1.00 1.00 1.00 1.05 0.95 1.05 0.95 1.05 1.05 1.00 1.05 1.05 0.95 1.00 1.00 0.95 0.95 0.95 1.05 1.05 1.05
MC
0.9 1.06 1.07 0.94 1.00 1.00 1.07 0.94 1.07 0.94 1.07 0.94 1.14 0.88 0.94 1.07 0.88 1.00 1.00 0.94 1.07 1.00 1.00 1.00 1.00 1.00 1.00
Vh 100 61 0.95 1.05 1.00 1.00 1.00 1.00 0.95 1.05 0.95 1.05 0.95 1.05 0.95 1.00 1.05 1.05 0.95 1.00 1.00 0.95 0.95 0.95 1.05 1.05 1.05
MC
0.9 1.27 1.06 0.94 1.00 1.00 1.06 0.94 1.06 0.94 1.06 0.94 1.10 0.89 1.10 1.06 0.89 1.00 1.00 0.94 1.06 1.00 1.00 1.10 1.00 1.00 0.89
Vh 20 13 0.90 1.11 0.95 1.06 1.00 1.00 0.95 1.05 0.84 1.16 0.95 1.05 0.90 1.06 1.11 1.11 0.90 1.06 0.95 0.95 0.84 0.84 1.05 1.16 1.16
MC
0.9 0.92 1.05 0.95 0.99 1.01 1.07 0.94 1.07 0.94 1.04 0.96 1.14 0.88 1.13 1.08 0.89 1.02 0.99 0.95 1.06 1.00 0.98 1.11 1.00 1.03 0.90
Table 6.5 Error analysis for varying distances. The first three rows indicate the relative change in distance for the axial downstream, upstream and
tangential position, respectively. The second column shows the absolute results obtained by Sapflow+ for a Vh of 50, 100 and 20 cm h-1 and an MC of 0.9
implemented in FEM with wounding. The lower rows show the relative change in Vh and MC due to the positioning errors for these values of V
h and MC.
Chapter 6
126
6.4.2 Comparison of Sapflow+ with other heat pulse methods
Similar to previous studies (Swanson, 1983; Green et al., 2003), the FEM results
(Figure 6.4) show that the Tmax and CHP method are limited in determining
negative or low heat velocities (<5 cm h-1), which was also confirmed for the CHP
method in the artificial stem segment data (Figure 6.9a). Moreover, both Tmax and
CHP underestimate Vh even without modelled wound effects. For the CHP method,
this was expected, as the applied equation is not strictly valid for non-ideal pulses,
which can be seen as a general shortcoming of the method because, in practice,
pulses will never be ideal. Apparently, the Tmax method is more sensitive to the
probe material than the Sapflow+ or HR method, for which the results agree closely
with the 1:1 line without wounding. The HR method, furthermore, can resolve
reverse and low heat velocities (Figure 6.6, Figure 6.10a) and agrees well with
Sapflow+ for the stem segment measurements (Figure 6.11), but shows deviations
for high heat velocities (>110 cm h-1) in the modelling results (Figure 6.6). For these
high heat velocities, the HR heat velocity levels off or even decreases as ∆Tup
remains approximately the same, whereas ∆Tdown
slightly decreases between 60 and
100 s (Figure 6.7). Shifting the time period for which the average HR signal was
calculated led to only slightly better results for the higher heat velocities; this was
also indicated by Green et al. (2009), who stated that shorting the averaging window
or altering the probe spacing will not largely improve the measurement range of the
HR method. Moreover, for very high heat velocities, the ∆Tup
signal becomes so small
that the ∆Tdown
/∆Tup
signal reaches extremely high values, leading to unrealistic high
heat velocity results. In practice, these flaws will worsen the applicability of the HR
method as ∆T signals below 0.02 °C are smaller than the detection limit of most
thermometric systems. Generally, a maximum heat velocity of approximately 55 cm
h-1 is presumed measurable with the HR method (Swanson, 1983; Burgess et al.,
2001a). A similar experiment for segments which allow higher sap flux densities
would be beneficial to assess the difference between HR and Sapflow+ for higher
flows. For these flows, the Sapflow+ method could make a difference, as it does not
suffer from these sensitivity problems because, similar to the HFD method, three
measurement needles are applied. This way, heat velocity can be accurately
determined across the entire range of sap flux densities when applying a correct
wound correction (Figure 6.5, Figure 6.9a). Given the symmetric positioning of the
The Sapflow+ method
127
axial temperature sensors, it can be assumed that good results will also be obtained
for reverse flow in stem segments as the only difference will be that the upstream
sensor needle will become the downstream needle and vice versa. The smaller
underestimation for the artificial stem segment in comparison with the stem
segments (Figure 6.9a, Figure 6.10a) is probably a result of the larger pores, allowing
water to continue its flow path more easily around the sensor needles which results
in a smaller wound effect.
In addition to its applicability across the entire range of sap flux density, the
Sapflow+ method has the advantage that, unlike the Tmax or HR method, thermal
diffusivity does not need to be determined separately as it is included in the model
calibrations. Hence, thermal diffusivity will be a model output instead of an input,
which is known to be prone to errors (Green et al., 2003; Vandegehuchte & Steppe,
2012a). Another advantage is that the water content is simultaneously estimated
with heat velocity with Sapflow+, at least for low flows ranging between -15 and 45
cm h-1. Hence, unlike other methods which determine the sap flux density from the
heat velocity by measuring the sapwood water content only once (taking a
destructive wood core), Sapflow+ should enable regular updates of water content
values which will lead to more accurate sap flux densities. At higher heat velocities,
less heat is transported tangentially and radially, resulting in a narrower and axially
longer heat field in comparison with lower heat velocities. As the area in which flow
is interrupted by wounding lays within this narrow zone, the influence of this area
will become more important, in comparison with a more broad heat field for lower
heat velocities. When applying the non-linear correction (Figure 6.8), even
estimations of water content changes at higher heat velocities can be made,
although these will probably be less accurate as wound effects may vary depending
on wood characteristics.
6.4.3 Challenges for the Sapflow+ method
The regression results for the separate stem segments show clear differences (Table
6.4). This is probably a result of radial and azimuthal variation in flow within the
segments. As not only variation between trees but also within the sapwood of a
single tree can occur as a result of stress factors, measurements at different depths
seem indispensable. The application of multiple thermocouples at different depths
could easily solve this, as has been shown for the HR method, for which the
Chapter 6
128
commercial sensors enable measurements at two radial depths. Hence, given a more
complicated fabrication of the sensors, Sapflow+ should be able to allow
measurements at multiple depths. However, for ring-porous species with a marked
distinction in early and late wood, additional correction factors might be necessary,
similar as for other heat pulse methods (Chapter 2). In general, further validation of
the method on different species and at a wider range of flows is necessary.
Another challenge lays in the accurate determination of MC. While at low flows the
deviation from the gravimetric results seems acceptable (Figure 6.10), at higher
flows the error is much larger. Even though a wound correction equation can reduce
these errors, such an equation depends on the obstructed zone caused by needle
installation which is dependent on sapwood properties. As the size and shape of
this wound zone is not known in practical applications, MC determination at higher
flows will be subject to large uncertainties. Validation experiments in combination
with for instance Frequency Domain Reflectometry measurements should be
conducted to test the accuracy of MC determination during low and high flows.
A more practical issue is the design of the sensor. As applied in this study, the
sensor’s operational system is an adapted CR1000 logger. This system is, however,
not applicable in field conditions as it requires constant line voltage, has impractical
dimensions and necessitates laborious data analysis. Therefore, a stand-alone
sensor and coupled software should be developed which allows field applications
and rapid data-analysis.
6.5 Conclusions
Overall, the results indicate that Sapflow+, by combining a three needle design
similar to the HFD method with the strengths of a heat pulse regime as applied by
the HR, CHP and Tmax method, performs well in determining heat velocity across
the entire naturally occurring sap flow range (approximately -15 to 110 cm3 cm-2 h-1).
Moreover, water content at low flows (Vh<45 cm h-1) can be estimated, necessary for
the conversion of heat velocity to sap flux density. Nevertheless, wound corrections
are required to overcome underestimations of heat velocity and water content
determinations at higher flows. Thus far, existing wound corrections for the current
available sap flow measurement methods are based on models similar as the FEM
used in this study (Swanson & Whitfield, 1981; Burgess et al., 2001a). However, as
The Sapflow+ method
129
wound effects seem to play a significant role in the performance of heat pulse based
sensors and the correction factors that need to be applied, further research on this
topic seems essential to obtain even more accurate results. It seems likely that
wound effects not only depend on needle diameters, but also on wood
characteristics which vary between and within tree species and might be influenced
by the heating process itself. Therefore, a combination of modelling, gravimetric
validation experiments and more advanced methods, such as MRI should be applied
to increase our knowledge on these wound phenomena and enable accurate wound
corrections for different wood types.
131
7 7 Practical application of the
Sapflow+ method in mangrove
water research
After: Vandegehuchte, M.W., Guyot, A., Hayes, M., Welti, N. Lockington,
D. & Steppe, K. (2012). Opposite daily stem diameter changes for co-occuring
mangrove species raise questions on environmental and endogenous growth
control. In preparation.
Chapter 7
132
7.1 Introduction
Mangroves grow worldwide in tropical and subtropical regions at the intertidal
zones between land and sea. While only occupying a global area of approximately 13
million ha, their north-south distribution, ranging from ca. 30°N to ca. 38°S, is large
(Quisthoudt et al., 2012) (Figure 7.1).
Their morphological and physiological flexibility allows mangroves to occupy areas
with large gradients in salt concentration (from oligohaline, with a salinity ranging
between 0.5 to 5 ppt to hyperhaline, with a salinity over 40 ppt ), substrate type
(from clayey to sandy sediments) and inundation regime (from twice a day to twice a
month or less) (Quisthoudt et al., 2012). Even though mangrove species show
common characteristics such as an extensive, shallow root system and salt
exclusion techniques, specific adaptations differ along mangrove species, often
resulting in typical zonation patterns (Krauss et al., 2008) with Rhizophora generally
restricted to the seaward side of the mangrove forest where soil water salinity and
inundation frequency are rather constant, while Avicennia can occur along the entire
intertidal zone.
The harsh environment, in which mangrove trees thrive, hinders water uptake and
plant growth in general. Mangrove soils are often high in organic matter, but
frequent inundation leads to slow decomposition and a low release rate of inorganic
nitrogen and phosphorus (Wanek et al., 2007). Moreover, flooding causes the soil to
become oxygen deficient and leads to accumulation of chemical compounds which
Figure 7.1 World map of the mangrove latitudinal limits (indicated by dots) for the two most
widespread mangrove genera Avicennia (full dots) and Rhizophora (open dots). AEP: Atlantic
East Pacific biogeographic region; IWP: Indo-West Pacific biogeograpic region (Quisthoudt et
al., 2012)).
Application of the Sapflow+ method in mangrove research
133
negatively affect plant growth (Barrett-Lennard, 2003; Colmer & Flowers, 2008). To
enhance oxygen uptake, mangrove species are equipped with aerial roots which
contain aerenchyma tissue, allowing rapid diffusion of oxygen from the lenticels to
submerged or underground roots (Purnobasuki & Suzuki, 2005).
Next to oxygen depletion, flooding also leads to high salinity levels. Two major salt
resistance mechanisms can be distinguished, allowing the regulation of cellular Na+,
Cl- and K+ concentrations (Drennan & Pammenter, 1982; Flowers & Colmer, 2008).
Rhizophora primarily excludes salt at root level, based on ultrafiltration of salt from
the water via tiny pores on the root system. Avicennia, on the other hand, allows the
uptake of salt water at root level, filtering the salt locally through semi-permeable
membranes and secreting the accumulated salt through excretion glands at leaf
level. Other morphological adaptations limit water loss at canopy level, such as
thick leaves with waxy cuticles (Rhizophora) and submerged stomata surrounded by
trichomes (Avicennia).
Because of their specific adaptations, mangrove species have been able to colonize
intertidal areas which remained inaccessible for most other species. In this intertidal
zone, mangrove communities form nurseries and breeding grounds for a wide range
of birds and marine organisms as they offer shelter and trap plant litter, leading to
decomposition into nutrients and, hence, providing food (Hogarth, 2007). Moreover,
mangrove forests have proven to be important for wood production, as a CO2 sink
as well as forming buffer regions against storms and tsunamis, protecting coastal
ecosystems (Cahoon et al., 2003; Stone, 2006; Duke et al., 2007). To fulfil these
essential functions, a dense structure in which healthy young trees are
complemented by healthy, sufficiently large, older trees is necessary (Duke et al.,
2007). Mangrove forests, however, are known to decline worldwide by 1 to 2 % a
year because of urbanization, aquaculture, coastal landfills or indirect effects of
pollution and climate change (Valiela et al., 2001; Duke et al., 2007). Despite the
need to protect mangroves, it is remarkable how little is known about the link
between water use and growth characteristics of many mangrove species in field
conditions, even though this key information seems indispensible to understand the
unique life traits of mangrove and to assess future changes in mangrove forest
density and dispersion. Becker et al. (1997) were the first to measure sap flux
density in mangrove species, later followed by Krauss et al. (2007), Hao et al. (2009)
and Muller et al. (2009). On the other hand, research has been conducted on
Chapter 7
134
mangrove stem growth based on growth ring analysis and stem diameter changes
(Downton, 1982; Schmitz et al., 2008; Alongi, 2011; Robert et al., 2011a; Robert et
al., 2011b). To our knowledge, however, no studies exist combining sap flow
measurements with stem growth patterns.
This chapter has the intention to investigate water use and coupled dynamic growth
of Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff. as examples of
the two most dominant mangrove genera Avicennia and Rhizophora. Additionally,
the experimental set-up allowed to test the Sapflow+ method in harsh field
conditions.
7.2 Materials and methods
7.2.1 Field site
Measurements were conducted at the west coast of North Stradbroke Island,
Queensland, Australia (S27°27.061’ E135°25.806’, Figure 7.2), a vegetated sand dune
island. The island is characterized by sandy soils and acidic waterbodies intertwined
by a complex mix of groundwater-fed lakes, swamps and creeks (Page et al., 2012).
These sandy soils and acidic waters lead to low nutrient availability in the mangrove
ecosystem (Rogers & Westman, 1977). According to the Köppen classification
(Kottek et al., 2006), North Stradbroke Island is subjected to a dry humid
subtropical climate, characterized by dry, cool winters and wet, humid summers. As
measurements were conducted during August and September 2012, dry conditions
were expected.
Figure 7.2 Location of the field site at the west coast of North Stradbroke Island, Queensland,
Australia.
20 km
10.58
km
2 km
Application of the Sapflow+ method in mangrove research
135
The field site was located in a long stretch of mangrove vegetation, dominated by
Avicennia marina (Forssk.) Vierh. (or grey mangrove) and Rhizophora stylosa Griff.
(or spotted red mangrove), intertwined by creeks, carrying fresh water from the
upstream inland tropical forest. On this field site, three full grown trees of both
Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff. were chosen, located
in proximity of each other to avoid tidal effects and spatial salinity gradients (Figure
7.3, Table 7.1). The field site was subjected to tidal movement, flooding the site
approximately twice every 24 hours.
1 m
MET
stationAv3
Av2
Av1
Rhi3
Rhi1 Rhi2
Beach at 25 m
N
Tree Av1 Av2 Av3 Rhi1 Rhi2 Rhi3
DBH (cm) 19.4 30.6 18.1 18.8 11.7 17.2
7.2.2 Meteorological data
Air temperature, relative humidity, shortwave solar radiation, rainfall and
windspeed were measured and recorded every ten minutes at 2 m above soil surface
(HOBO weather station, Onset, Cape Cod, Massachusetts, USA). Vapour pressure
deficit (VPD, kPa) was inferred from measured air temperature (Tair
) and relative
humidity (RH) according to Buck (1981):
0VPD e e (7.1)
Figure 7.3 Schematic of the measured trees at the mangrove site on the west coast of North
Stradbroke Island, showing the measured Avicennia trees (grey circles), the measured
Rhizophora trees (white circles) and the location of the weather station (MET station).
Table 7.1 Diameter at breast height (DBH) of the measured mangrove trees.
Tree line at ±100 m
Chapter 7
136
with e the air vapour pressure and e0 the saturated air vapour pressure, calculated
as:
0
17 276107
237 3
air
air
. Te .
T .
exp (7.2)
0e RH e (7.3)
Soil salinity and water table depth were determined with in situ pressure sensors
(Aqua Troll 200, In-Situ Inc., Fort Collins, CO, USA) installed in piezometers, located
close to the measured trees at depths of 25 and 180 cm. Actual measured soil water
conductivity (AC in mS cm-1) was converted to osmotic water potential
(MPa)
based on McIntyre (1980):
1 09110 . AC
log( )-1.46 (7.4)
7.2.3 Ecophysiological measurements
All trees were equipped with a dendroband (DRL26 – Logging Band Dendrometer,
ICT international, Armidale, NSW, Australia), continuously recording stem diameter
variations. Stem water potentials were recorded with stem psychrometers (PSY-1
Stem Psychrometer, ICT International, Armidale, NSW, Australia). These
psychrometers were cleaned and reinstalled as soon as the peltier curve indicated
that the thermocouples were soiled.
To assess sap flux density and sapwood water content, each tree was equipped with
a Sapflow+ sensor at the South side of the tree and a Heat Ratio sensor at the North
side. Sapwood cores were taken once to assess sapwood water content and dry
density gravimetrically and calculate the heat input of the Sapflow+ sensors as
described in Chapter 6. As the Sapflow hardware applied in Chapter 6 was not
practical to use in field conditions, a stand-alone logger was developed for each
Sapflow+ sensor. During instalment of the sap flux density sensors, the bark was
removed to ensure that the sensor needles were completely inserted in the
sapwood. The HR sensors measured sap flux density at 0.75 cm and 2.25 cm below
the cambium while the Sapflow+ sensors measured at depths of 1.5 cm and 2.5 cm
below the cambium. The HR sensors measured sap flux density each 15 min while
the Sapflow+ sensors had a frequency of one measurement each 40 minutes, the
time necessary for the heat generated by the hand-made heaters to be fully
Application of the Sapflow+ method in mangrove research
137
dissipated. As the main interest of the research concerned relative patterns, we
chose not to convert measured heat velocity to sap flux density. This way, errors
because of the conversion to sap flux density based on MC and wounding were
avoided. Nevertheless, wound widths for both species were measured based on the
cutting of three branch segments per species in which example holes were drilled.
This resulted in average wound widths of 1.63±0.02 mm for Avicennia and
1.58±0.04 for Rhizophora.Besides these continuous measurements, stomatal
conductance was measured hourly approximately from sunrise till two hours after
sunset during four days (DOY 241, 247, 251 and 254) throughout the measurement
period, applying a dynamic porometer (AP4 dynamic porometer, Delta-T Devices
Ltd, Cambridge, UK) on Av1, Av3, Rhi2 and Rhi3. For every measurement, the
average of three leaves located close to each other was taken. Measurements were
always conducted on the same leaves throughout the day as well as for the different
measurement days.
7.2.4 Dynamic stem growth model
By slightly modifying the mathematical flow and storage model of Steppe et al.
(2006), a mechanistic model was obtained to assess dynamics in xylem and storage
water potentials based on stem sap flux density and stem diameter variations
(Figure 7.4). This model was applied as a tool to synthesise the conducted
measurements and derive trends in osmotic potential of the stem storage tissue.
Chapter 7
138
1 exp outS a( (b D ))
2in outD D S
22 2st outV l( D S S )
0 4st st wW . V
exp outout
dDd Sab ( b D )
dt dt
2outin dDdD d S
dt dt dt
2 2st outout
dV dD d S d Sl S D S
dt dt dt dt
st stw
dW dV
dt dt
st
p
0
0
st st
p out p st ststout p p
st
d DdVD
dt dt V
0
st st
p out pst
st
d DdV
dt dt V
x r xSF R
r
soil soilk
1st
inR D L
st x ststdWR
dt
st st st
p
Stem flow and storage model
Stem diameter variation submodelStem water transport
submodel
Growth?
NO YES
Figure 7.4 Schematic overview of the model linking the dynamics of stem diameter variations
to stem sap flow and storage. The links between the two submodels as mentioned in the text
are indicated by arrows. Measurements of Dout
form the input of the stem diameter submodel
while the water transport submodel is run on SF measurements. Symbols are explained in the
List of abbreviations and symbols and in the text.
Application of the Sapflow+ method in mangrove research
139
In this model, the thickness of the stem storage compartment ∆S (m) is linked to the
outer stem diameter Dout
(m) via an empirical relationship (Génard et al., 2001;
Steppe et al., 2006):
1 exp outS a( (b D )) (7.5)
with a and b empirical parameters. Based on measurements of bark thickness and
stem diameter of the investigated Avicennia and Rhizophora trees, rough estimates
of a and b were obtained, with a=0.0035 and b=18.47 m-1 for Avicennia and
a=0.0153 and b=10.03 m-1 for Rhizophora, respectively. From ∆S and the measured
Dout
, the inner diameter of the stem Din consisting of the outer diameter minus the
storage tissue can be calculated, as well as the water flow (dVst/dt in m³ s-1) in and
out of the stem storage tissue, with l (m) the length of the stem which was measured
for both species. This Vst is directly linked to the storage tissue pressure water
potential st
p , distinguishing between elastic growth (st
p ) (Eq. 7.6) or both
elastic and plastic growth (st
p ) (Eq. 7.7) (Lockhart, 1965):
st
pst st
el
ddV V
dt dt
(7.6)
st
p stst stst p
el pl
ddV VV
dt dt
(7.7)
with the extensibility of cell walls in relation to non-reversible dimensional
changes (MPa-1s-1), the bulk elastic modulus of living tissue in relation to reversible
dimensional changes (MPa) and the critical value (in MPa) for the pressure
component (st
p ) which must be exceeded to produce (positive) growth in the
storage compartment. For this threshold pressure , different values have been
observed, ranging from 0.1 to 0.9 MPa (Green et al., 1971; Green & Cummins, 1974;
Hsiao & Xu, 2000). Based on the reasoning of Génard et al. (2001) that Γ has to be
higher for stem tissues than for the young tissues or individual cells on which most
of the measurements have been made, the upper value of 0.9 MPa was chosen for
the simulations.
Chapter 7
140
The bulk elastic modulus is considered proportional to Dout
and st
p :
0
st
out pD (7.8)
with 0 a proportionality constant (Génard et al., 2001; Steppe et al., 2006).
The obtained variables from this diameter driven growth submodel can then be
applied in the water transport submodel. In this submodel xylem water potential
x (MPa) is derived from the root water potential r (considered proportional to
the soil water potential soil applying a proportionality factor ksoil
), the measured sap
flow SF (mg s-1) and the xylem resistance to flow Rx (MPa s mg-1). Rx and ksoil
can be
calibrated based on stem water potential measurements. If x is known, the water
potential of the storage tissue can be determined based on the flow to and from this
compartment and the exchange resistance Rs (MPa s mg-1) between stem storage and
stem xylem compartments. The latter is determined based on the assumption that
the stem storage and xylem compartments are separated by a virtual membrane
with a radial hydraulic conductivity L (m MPa-1 s-1) (Steppe et al., 2006). The mass
flow of water to and from the storage compartment is determined from the
volumetric flow assuming a constant water density of 1000 kg m-3 and taking into
account that only 40 % of the total stem storage volume Vst consists of water (Steppe
et al., 2006). Knowing the pressure water potential of the storage tissue from the
diameter submodel, the osmotic water potential of the storage tissue st
can then
be derived.
While ksoil
and Rx can independently be assessed through calibration of the modelled
xylem water potentials based on the psychrometric measurements, the parameters
L, and 0 remain unknown. Also, an initial value of
st
p must be fed to the model.
For L, values obtained from cells of higher plant tissues between 1.1×10-10 and
1.67×10-4 m MPa-1s-1 have been mentioned (Dainty & Preston, 1963; Dale & Sutcliffe,
1986). For cell wall extensibility , Hsiao et al. (1998) mention a range from 8.33×10-
6 to 5.56×10-5 for young plants, although for older tissues this the extensibility is
likely to be an order of magnitude lower (Génard et al., 2001). The elastic modulus
ranges from from 0 to 30 MPa for higher plant tissues (Dainty & Preston, 1963;
Application of the Sapflow+ method in mangrove research
141
Dale & Sutcliffe, 1986), allowing a realistic estimation of 0 based on D
out and
st
p
values. For the initial value of st
p , st( in)
p , a value of 0.7 was applied.
From the derived st
and V
st, a measure for the total amount of osmotic active
compounds Neq (mol) in the storage tissue can be derived from the Van ‘t Hoff
equation (Eq. 1.3):
eq stN VRT
(7.9)
As no distinction is made between the different compounds or their osmotic
activity, Neq will be referred to as a number of osmotic equivalents.
The model, consisting of a set of algebraic and differential equations, was
implemented, simulated and calibrated using the modelling and simulation
software package PhytoSim (Phyto-IT BVBA, Mariakerke, Belgium). Table 7.2
shows the applied parameter values, based on Génard et al. (2001) and Steppe et
al. (2006).
Parameter Value
L (m MPa-1 s-1) 2.85×10-9
(MPa-1 s-1) 2.34×10-7
0 (m-1) 150
Table 7.2 Applied model parameters. These parameters were chosen within the ranges
mentioned in literature, based on expert knowledge.
Chapter 7
142
7.3 Applicability of the Sapflow+ method in field conditions
7.3.1 Results
Heat velocity
Unlike in Chapter 6, it was not possible to set up a gravimetric validation
experiment at the mangrove site. Therefore, the Sapflow+ method was compared to
the HR method (Figure 7.5). Although a high correlation was obtained between the
Sapflow+ Vh measurements and those of the HR sensors (correlation coefficient
0.83), a pooled regression of all measured data did not lead to a clear linear relation
(R²=0.68) (Figure 7.5a). However, when regressing these measurements for each tree
separately, an average R² of 0.93±0.05 was obtained. Moreover, when applying Eq.
6.9 to the downstream and upstream temperatures measured by the Sapflow+
sensor, even the pooled data led to a good linear fit (Figure 7.5b).
-5 0 5 10 15 20 25
Vh H
R (
cm
h-1
)
-2
0
2
4
6
8
10
12
14
16
Vh SF+_HR=0.1+0.96Vh SF+R²=0.99
Vh SF+ (cm h-1)
-5 0 5 10 15 20 25
Vh S
F+
_H
R (c
m h
-1)
-5
0
5
10
15
20
25
(a) (b)
Figure 7.5 (a) Heat velocity Vh as determined by the HR sensors versus V
h determined by the
Sapflow+ (SF+) sensors for all measured trees, both Avicennia and Rhizophora; and (b) Vh as
determined applying the HR method to the downstream and upstream temperature
measurements of the Sapflow+ sensor (Vh SF+_HR) versus V
h determined by the Sapflow+
sensor, both for Avicennia and Rhizophora. For the application of the HR method to the
Sapflow+ temperature measurements, Dax values as obtained by the Sapflow+ method were
applied.
Application of the Sapflow+ method in mangrove research
143
Water content
Figure 7.6a, c indicates that Vh and MC patterns are highly correlated (correlation
coefficient of 0.90), with MC showing a daily pattern similar to the Vh pattern: when
daily peaks were registered for Vh, also peaks in MC were noted both for Avicennia
and Rhizophora (Figure 7.6a, b), while for those depths for which Vh did not vary,
also no daily variation in MC was registered for both species (Figure 7.6c, d).
However, while Vh measured according to the Sapflow+ method showed no noise
throughout the entire measurement period, MC data became noisier even though Vh
patterns remained accurate (Figure 7.6b, d). While for some installed sensors, this
noise only occurred after more than a month, for others it emerged already after a
week. Nevertheless, despite this noise the observed MC patterns were still somehow
visible and remained unaltered throughout the measurement period.
226 227 228 229 230 231 232
0.0
0.2
0.4
0.6
0.8
Y A
xis
2
MC
Vh
MC
SF
+
0.2
0.4
0.6
0.8
1.0
Vh
SF
+ (c
m h
-1)
0
5
10
15
20
25
Day of the year
242 243 244 245 246 247 248
0
5
10
15
20
25
(a) (b)
(c) (d)
Figure 7.6 Examples of water content (MC, black dots) and heat velocity (Vh, grey line)
measured according to the Sapflow+ method at the beginning of (a, c) and later on during the
measurement period (b, d). While a and b show measurements at an outer measurement point
where sap flux density showed a clear daily pattern, c and d show measurements at an inner
measurement point where there was very little variation in sap flux density. MC values were
corrected for flow effects based on the wound corrections mentioned in Figure 6.8 and Figure
6.9.
Chapter 7
144
As daily measurements of MC may be prone to errors, the nightly average of the MC
values from 19.30 till 5.00 h was determined to investigate the long term changes in
stem water content. To this end, data of subsequent days measured with the same
sensor were analyzed. Figure 7.7 shows nightly water content for Avicennia 3 and
Rhizophora 3. To assess long-term rise or decline in water content, a weighted linear
regression was conducted. This led to significant slopes of 0.1±0.03 % per day for
Avicennia 1, 0.07±0.02 % per day for Avicennia 3 and -0.05±0.01 % per day for
Rhizophora 3 while for the other trees the slope did not significantly differ from
zero.
7.3.2 Discussion
Heat velocity
As it is known that sap flux density and, hence, heat velocity can greatly vary
radially and azimuthally (Ford et al., 2004; Krauss et al., 2007; Saveyn et al., 2008), it
was not surprising that the pooled dataset of all Sapflow+ Vh measurements did not
lead to a good linear relation with the HR Vh measurements as both sensors
measured at different depths and different time intervals (Figure 7.5a). The high
correlation coefficient of the pooled dataset and the good linear regressions for
Day of the year
220 230 240 250 260 270 280
Wate
r conte
nt
(kg
wa
ter kg
dry
we
igh
t-1)
0.0
0.2
0.4
0.6
0.8
1.0
Av3
Rhi3
Figure 7.7 Water content determined as the average of night-time (19.30 - 5.00 h) water
content measurements. Av3 and Rhi3 were chosen as for these trees, the longest
uninterrupted measurements with the same sensor were obtained.
Application of the Sapflow+ method in mangrove research
145
each tree separately, however, indicated that the Sapflow+ sensors were able to
capture the same trends in Vh as the HR sensors. This was clearly confirmed when
comparing the Sapflow+ data with those obtained by applying the HR method on the
temperatures measured upstream and downstream with the Sapflow+ sensor (Figure
7.5b). These results are in agreement with the results from Chapter 6, showing that
the Sapflow+ and HR method perform equally for reverse to moderate flows. As the
highest measured Vh was 24 cm h-1, possible discrepancies between Sapflow+ and HR
measurements at higher flows could not be confirmed.
Unlike the theoretical calculations in Chapter 6, the Sapflow+ results and HR results
applying the measurements from the Sapflow+ sensor are not exactly equal as the
linear regression led to an offset of 0.1 and a slope of 0.96. This is probably because
of small differences between the actual needle distances and those measured and
applied in the Vh calculations as it has been shown that small offsets in needle
spacing can lead to large differences in Vh determination, both for the Sapflow+ and
the HR method (Chapter 6).
For the rest of this chapter, Vh values determined according to the Sapflow+ method
will be used. However, because of practical issues, some gaps occurred in the
Sapflow+ data. For these periods (approximately 11% of the data), Vh data were
interpolated based on the HR results obtained by the HR sensor from the same tree.
Water content
On an hourly time scale, MC clearly increased during the day when sap flow rose
and decreased again when sap flow declined. This is somewhat counterintuitive as it
is known that for most species MC should decline during the day and rise during
the night because of the lag between transpiration and sap flow (Jameson, 1966;
Borghetti et al., 1991). Moreover, the daily fluctuations in MC seem very large (up to
20 %). Nevertheless, similar patterns have been shown for gravimetric
measurements on twigs of Pinyon species during dry winters, although this pattern
was not physiologically explained (Jameson, 1966).
The observed noise is likely due to sensor properties which need further
improvement. As such, it was noted that the applied heaters slowly corroded
leading to unequal heat pulses and finally heater breakdown. As MC is much more
sensitive towards heat input than Vh, small changes in heat input can affect MC
results without affecting Vh. Additionally, MC is more closely correlated to thermal
Chapter 7
146
conductivity which in practice may lead to identifiability problems, even though
theoretically the model is identifiable (Chapter 6). Optimization of the hardware and
a thorough comparison of the model parameters may further improve MC
measurements.
On the longer term, however, MC results were readily interpretable. These results
indicated that there was little change in water content throughout the measurement
period. Even though these results could not be confirmed by an independent
validation, the obtained nightly averages seem realistic and the long-term patterns
plausible. As such, these long-term patterns can be coupled to other
ecophysiological variables when assessing the water use strategies of the species
under investigation.
7.4 Water flow and storage in Avicennia and Rhizophora
7.4.1 Results
Given the similar patterns in the ecophysiological variables for the three trees of
each species, the average of the three trees per species was taken for further
analysis. This way, a more general investigation of species water use was conducted,
rather than focussing on intra-species variability.
Ecophysiological measurements
Averaged heat velocity showed a good positive correlation with both radiation
(correlation coefficients of 0.83 and 0.78 for Avicennia and Rhizophora,
respectively) and VPD (correlation coefficients of 0.86 and 0.88 for Avicennia and
Rhizophora, respectively) (Figure 7.8). As soil water potential, at both measured
depths, varied very little with an average value of -2.1 MPa and a standard deviation
of only 0.1 MPa, heat velocity and soil water potential were not correlated, with
correlation coefficients 0.08 and 0.04 for Avicennia and Rhizophora, respectively
(Figure 7.8). While stomatal conductance for Rhizophora was very low during the
night and increased during daytime, the reverse pattern was measured for
Avicennia, showing large stomatal conductance at night-time. On average, stomatal
conductance values for Avicennia were higher than for Rhizophora (Figure 7.9).
While average heat velocity patterns were closely correlated for Avicennia and
Rhizophora (correlation coefficient 0.91), their stem diameter changes were
Application of the Sapflow+ method in mangrove research
147
markedly different (Figure 7.8c, d). While Avicennia showed the classical pattern
where the diameter decreases in the morning and increases at night, diameters for
Rhizophora increased during the morning and decreased in the late afternoon,
remaining more or less stable at night-time. Stem water potentials for both species
were again similar, decreasing in the morning and increasing in the afternoon.
Chapter 7
148
Heat velo
city
Vh (
cm
h-1
)
0
2
4
6
8
10
Ste
m d
iam
ete
r (cm
)23.000
23.005
23.010
Soil
wate
r pote
ntial (M
Pa)
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
Wate
r level
above s
oil (m
)0.0
0.2
0.4
0.6
Sola
r ra
dia
tion (
W m
-2)
0
200
400
600
800
1000
VP
D (k
Pa)
0
5
10
15
20
25Radiation
VPD
(a)
(b)
(c)
(d)
(e)
Heat velo
city
Vh (
cm
h-1
)
0
2
4
6
8
10
Ste
m d
iam
ete
r (cm
)
16.188
16.190
16.192
16.194
16.196
16.198
16.200
Day of the year
246 247 248 249Ste
m w
ate
r pote
ntial (M
Pa)
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
Soil WP
Water level
Diameter Rhizophora
Vh Rhizophora
Diameter Avicennia
Vh Avicennia
Stem WP Rhizophora
Stem WP Avicennia
Figure 7.8 Shortwave solar radiation and vapour pressure deficit (VPD) (a); Soil water
potential and water level above the soil (c); heat velocity Vh and diameter change for Avicennia
(c) and Rhizophora (d) and stem water potential for Avicennia and Rhizophora (e) during
standard days.
Application of the Sapflow+ method in mangrove research
149
On 5 different days (DOY 231, 238, 245, 252, 258) throughout the dry measurement
period (no rain fell from DOY 224, the start of the measurement campaign, till DOY
262), a steep decline in average stem diameter of both Avicennia and Rhizophora
was noted (Figure 7.10 as an example). During these days, the stem diameter of
Rhizophora hardly increased or even decreased in the morning and further
decreased in the afternoon while for Avicennia, the decrease in diameter was much
larger than on standard days. During these days, it was noted that the VPD values
were higher during the morning and/or during the afternoon compared to standard
days, which was reflected in a steeper decline of stem water potential and
corresponding rise of heat velocity in the morning and vice versa in the afternoon.
Time (h)
05 09 13 17
Sto
mata
l conducta
nce A
vic
ennia
(m
m s
-1)
0
2
4
6
8
Sto
mata
l conducta
nce R
hizo
phora
(mm
s-1)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Avicennia
Rhizophora
Figure 7.9 Stomatal conductance for Avicennia and Rhizophora, determined as the average
of measurements conducted during 4 standard days (DOY 241, 247, 251 and 254) during the
dry period.
Chapter 7
150
So
lar
radia
tio
n (
W m
-2)
0
200
400
600
800
1000
VP
D (k
Pa
)
0
5
10
15
20
25S
oil
wa
ter
pote
ntia
l (M
Pa
)
-3.5
-3.0
-2.5
-2.0
-1.5 Wa
ter le
ve
l
abo
ve
so
il (m)0.0
0.2
0.4
0.6Soil WP
Water level
Hea
t ve
locity
Vh (
cm
h-1
)
-2
0
2
4
6
8
10
Ste
m d
iam
ete
r (cm
)
22.995
23.000
23.005
23.010
Day of the year
252 253 254 255Ste
m w
ate
r p
ote
ntia
l (M
Pa
)
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
(a)
(b)
(c)
(d)
(e)
Hea
t ve
locity
Vh (
cm
h-1
)
0
2
4
6
8
10
Ste
m d
iam
ete
r (cm
)
16.188
16.190
16.192
16.194
16.196
16.198
16.200
Radiation
VPD
Diameter Avicennia
Vh Avicennia
Diameter Rhizophora
Vh Rhizophora
Stem WP Rhizophora
Stem WP Avicennia
Figure 7.10 Shortwave solar radiation and vapour pressure deficit (VPD) (a); Soil water
potential and water level above the soil (c); heat velocity Vh and diameter change for Avicennia
(c) and Rhizophora (d) and stem water potential for Avicennia and Rhizophora (e) during a
period with a typical diameter decline.
Application of the Sapflow+ method in mangrove research
151
Modelled storage water potential patterns
In Figure 7.11 the model results of the standard conditions are shown. While for
Avicennia, the storage water potential lags behind the xylem water potential,
corresponding with a decreasing stem diameter in the morning and an increase of
stem diameter in the afternoon, the reverse pattern is visible for Rhizophora. This
difference in total storage water potential is caused by the time lag in storage
osmotic water potential (Figure 7.12a). Although the patterns are very alike, the
number of osmotic equivalents increases more rapidly for Rhizophora compared to
Avicennia (Figure 7.12b).
2D Graph 1
246.0 246.5 247.0 247.5 248.0 248.5 249.0
Wate
r pote
ntial (M
Pa)
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
2D Graph 1
Ste
m d
iam
ete
r (cm
)
22.998
23.000
23.002
23.004
23.006
23.008
23.010
Xylem
Storage
Diameter
Day of the year
246.0 246.5 247.0 247.5 248.0 248.5 249.0
Wate
r pote
ntial (M
Pa)
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
246.2 246.4 246.6 246.8 247.0 247.2
Ste
m d
iam
ete
r (cm
)
16.191
16.192
16.193
16.194
16.195
16.196
(a) (b)
(c) (d)
Figure 7.11 Model results showing the diameter input and xylem and storage water potential
output for both Avicennia (a, b) and Rhizophora (c, d) during standard conditions. (b) and (d)
are more detailed representations of the model results for a single day.
Chapter 7
152
For the days where a strong decline in stem diameter was observed, the xylem water
potential became more negative, enlarging the difference with storage water
potential for Avicennia and narrowing this difference for Rhizophora in the
morning, resulting in a stronger decline and less increase in stem diameter for both
species, respectively (Figure 7.13). In the afternoon, the more negative xylem
potential led to a larger difference with the storage water potential for Rhizophora,
magnifying the afternoon shrinkage. While both species show an increase in osmotic
equivalents in the stem storage volume (Figure 7.14), the osmotic potential remains
insufficiently negative to avoid the diameter decline.
(M
Pa)
Avic
ennia
-4.6
-4.4
-4.2
-4.0
-3.8
-3.6
-3.4
-3.2
(M
Pa) R
hiz
ophora
-4.2
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
-2.8
Day of the year
246.0 246.5 247.0 247.5 248.0 248.5 249.0
Osm
otic e
quiv
ale
nts
Avic
ennia
(m
ol)
24
26
28
30
32
34
Osm
otic
equiv
ale
nts
Rhiz
ophora
(mol)
24
26
28
30
32
34
Avicennia
Rhizopora
(a)
(b)
Figure 7.12 Osmotic potential of the storage tissue (a) and derived osmotic equivalents (b) for
Avicennia and Rhizophora during standard conditions.
Application of the Sapflow+ method in mangrove research
153
Wate
r pote
ntial (M
Pa)
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
Day of the year
252.0 252.5 253.0 253.5 254.0 254.5 255.0
Wate
r pote
ntial (M
Pa)
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
Ste
m d
iam
ete
r (cm
)
22.998
23.000
23.002
23.004
23.006
23.008
252.2 252.4 252.6 252.8 253.0
Ste
m d
iam
ete
r (cm
)
16.190
16.191
16.192
16.193
16.194
16.195
16.196
Xylem
Storage
Diameter
(a) (b)
(c) (d)
Figure 7.13 Model results showing the diameter input and xylem and storage water potential
output for both Avicennia (a, b) and Rhizophora (c, d) during diameter decline conditions (with
a typical diameter decline during DOY 252). (b) and (d) are more detailed representations of
the model results for a single day.
Chapter 7
154
Rain events
Despite their remarkably different growth pattern, stem diameters of both
Avicennia and Rhizophora showed an immediate increase during rain events (Figure
7.15 as an example of the first rain event). During rainfall at daytime, sap flux
density fell to zero while xylem water potential and stem diameter for both species
increased. However, also during night-time, when sap flux density was already zero
(or close to zero during high night-time VPD for Avicennia), the stem diameter of
both species rose rapidly. These rain events were crucial as each time, an increase in
diameter of more than double the standard difference in daily maximum and
minimum was obtained, muting the gradually decline in stem diameter for
Avicennia and even leading to stabilization for Rhizophora (Figure 7.16).
(M
Pa
) A
vic
enn
ia
-4.2
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
(M
Pa
) Rh
izo
ph
ora
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
-2.8
Day of the year
252.0 252.5 253.0 253.5 254.0 254.5 255.0
Osm
otic e
qu
iva
lents
Avic
enn
ia (
mo
l)
22
24
26
28
30
32
34
Osm
otic
equ
iva
lents
Rh
izo
ph
ora
(mo
l)
24
26
28
30
32
34
36
Avicennia
Rhizophora
(a)
(b)
Figure 7.14 Osmotic potential of the storage tissue (a) and derived osmotic equivalents (b) for
Avicennia and Rhizophora during diameter decline conditions (with a typical diameter decline
during DOY 252).
Application of the Sapflow+ method in mangrove research
155
Sola
r ra
dia
tion (
W m
-2)
0
200
400
600
800
1000
VP
D (k
Pa)
0
2
4
6
8
10
12
14
16R
ain
(mm
)
0
1
2
3
4
Radiation
VPD
rain S
oil
wate
r pote
ntial (M
Pa)
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
Wate
r level a
bove s
oil (m
)
0.0
0.2
0.4
0.6Soil WP
Water level
Heat velo
city
Vh (
cm
h-1
)
0
2
4
6
8
22.99
23.00
23.01
23.02
Dia
mete
r Rhiz
ophora
(cm
)
16.190
16.195
16.200
16.205
16.210
16.215Vh Avicennia
Vh Rhizophora
Diameter Avicennia
Diameter Rhizophora
Day of the year
260 261 262 263 264 265 266
Ste
m w
ate
r pote
ntial (M
Pa)
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0Stem WP Avicennia
Stem WP Rhizophora
(a)
(b)
(c)
(d)
Dia
mete
r Avic
ennia
(cm
)
Figure 7.15 Shortwave solar radiation, vapour pressure deficit (VPD) and rain (a); Soil water
potential and water level above the soil (b); heat velocity Vh and diameter change for
Avicennia and Rhizophora (c) and stem water potential for Avicennia and Rhizophora (d)
during a period with rainfall.
Chapter 7
156
7.4.2 Discussion
Low flows: an indication of drought stress rather than proof against the
cohesion-tension theory
Similarly as suggested or measured in previous studies and reviews on mangroves
(Ball, 1988; Zimmermann et al., 1994; Krauss et al., 2007), measured heat velocities
and, hence, sap flux densities in our study were very low (maximal recorded heat
velocity of 24 cm h-1) (Figure 7.5, Figure 7.8, Figure 7.10, Figure 7.15). Zimmerman et
al. (1994; 2002) attributed these low flows to the presence of viscous, polymeric
substances in the xylem sap and hypothesized that these substances caused the
upward water flow by reducing the chemical activity of water. This hypothesis,
together with their pressure probe measurements which showed much less negative
xylem pressures than those obtained by the pressure bomb (Zimmermann et al.,
2004), led these authors to discard the widely accepted cohesion-tension theory (see
also Section 1.1.2). Becker et al. (1997), however, measured sap flux densities in
mangrove species which were very similar to those measured in a tropical heath
forest with a similar climate and concluded that sap flow rates of mangrove trees
are not necessarily unusually low. Although their experimental plot had freshwater
entering from streams and a sewer, it was not known if the trees relied on these
freshwater sources. As proven by isotope analysis, mangrove trees often do have
Day of the year
220 230 240 250 260 270 280 290
Ste
m d
iam
ete
r A
vic
ennia
(cm
)
22.98
22.99
23.00
23.01
23.02
Ste
m d
iam
ete
r Rhizo
pho
ra (c
m)
16.18
16.19
16.20
16.21
16.22
Rain
(mm
)
0
1
2
3
4
5
6
Avicennia
Rhizophora
Rain
Figure 7.16 Stem diameter of Avicennia and Rhizophora during the measurement period.
Application of the Sapflow+ method in mangrove research
157
access to freshwater lenses, enhancing water uptake (Lambs et al., 2008). It is,
hence, more plausible that the low sap flow rates noted in many mangrove studies
can be attributed to the high salinity of the available water, lowering the water
potential and thwarting water uptake. Given the very negative soil water potentials
(Figure 7.8, Figure 7.10) and the overall decline in stem diameter of both species
(Figure 7.16), the measured trees clearly suffered from drought stress. Hence, it is
not unexpected that these stressed trees want to reduce their water loss as much as
possible, resulting in low flows and rather low stomatal conductances during the
day (Figure 7.9). Moreover, the measured stem water potentials in this study show
that mangrove trees do establish highly negative stem water potentials, conform the
cohesion-tension theory.
Stem diameter variations: time lag and/or osmotic regulation?
When interpreting the plant water status, the radial transport between the xylem
and surrounding storage tissues is of crucial importance as it allows turgor to build
up which ultimately leads to plastic growth if a threshold pressure is overcome
(Lockhart, 1965). Moreover, water in the storage tissue buffers discrepancies
between water demand and supply. As such, it has been commonly accepted that a
clear time lag exists between the transpiration at leaf level and the water uptake at
root level, caused by the hydraulic resistance between the two (Zweifel et al., 2000;
e.g. Peramaki et al., 2001; Sevanto et al., 2002; Steppe et al., 2006) (see also Section
1.3.1 and Figure 1.11). This time lag causes a decrease in stem diameter in the
morning as then the water supply from the roots lags behind the transpiration at
leaf level, necessitating water flow from the storage compartments (Hinckley &
Bruckerhoff, 1975). In the afternoon, when xylem water potential rises because of a
decreased atmospheric water demand, water again flows back to the storage tissues,
resulting in a diameter increase (Molz & Klepper, 1973).
Despite this commonly accepted morning shrinking and afternoon swelling pattern
of trees, reverse diameter patterns as shown for Rhizophora (Figure 7.8d, Figure
7.10d) have been mentioned before for crasulacean acid metabolism (CAM) plants
(Gouws et al., 2005; Matimati et al., 2012). These CAM plants are characterised by
night-time acquisition of CO2 through open stomata, which is then stored as foliar
organic acids. During daytime, decarboxylation of these acids allows for
photosynthesis behind closed stomata (Osmond et al., 2008). However, the
Chapter 7
158
measurements of low night-time and higher daytime stomatal conductance coupled
with a daily sap flux density pattern clearly indicate that Rhizophora stylosa Griff.
cannot be considered a CAM plant (Figure 7.8d, Figure 7.9, Figure 7.10d).
For many, mostly herbaceous, species, daytime stem diameter increase can be noted
during conditions of very low to zero VPD and sufficient soil water availability. This
phenomenon is caused by the active loading of solutes into the xylem and
subsequent osmotic uptake of water and is termed root pressure (Kramer & Boyer,
1995). During conditions of low transpiration, the solutes retained in the
endodermis and transported to the xylem allow root pressure to build up, causing
an upward water flow which can then be radially transported to the storage tissues
(Steudle & Peterson, 1998). Even though for Avicennia early morning growth peaks
could be seen when VPD was zero and root pressure may have been present for both
species during these conditions, it cannot explain the daily growth pattern of
Rhizophora as diameter increase continued when VPD increased and xylem water
potential decreased (Figure 7.8, Figure 7.10). To our knowledge, a similar
combination of morning diameter increase and afternoon decrease together with a
classical sap flux density and stem water potential pattern has not been presented
in literature so far.
By which mechanism then, if not CAM or root pressure, do these differences in
growth pattern for both species, influenced by the same environmental conditions,
occur? The results of the mechanistic model based on the cohesion-tension theory,
show that the different growth patterns can be explained by a difference in time lag
between xylem and storage water potential (Figure 7.11, Figure 7.13) and suggest
that both species show a daily pattern of osmoregulation in the storage tissue
(Figure 7.12, Figure 7.14). A slightly earlier increase of osmotic active compounds in
the storage tissue, allows the storage compartments of Rhizophora to draw water
from the xylem during the morning, whereas for Avicennia, the slightly delayed
increase in osmotic compounds causes the storage water potential to be less
negative than the xylem water potential, resulting in diameter decrease (Figure 7.12).
If, however, VPD is high during the morning, xylem water potential decreases
relatively more than the storage water potential. Apparently, the osmotic regulation
of the storage tissue is not capable of compensating this drop in xylem water
potential, resulting in a stronger diameter decline for Avicennia and reduced
Application of the Sapflow+ method in mangrove research
159
diameter increase or even decrease for Rhizophora (Figure 7.10, Figure 7.13, Figure
7.14).
Rain as important growth factor
Despite the reversed daily diameter variation patterns of Avicennia and Rhizophora,
both species immediately showed a large diameter increase at the onset of rainfall
(Figure 7.15, Figure 7.16). While rainfall is known to induce stem diameter increase
as it leads to a sudden drop in xylem water potential, similarly as during stomatal
closure in the afternoon, here the growth peaks occurred both during daytime and
night-time rain events, implying another mechanism. As the diameter responses
were immediate, whether at high or low tide, and sap flux density was zero during
these growth peaks, also rain water uptake from the soil can be excluded. This
leaves direct canopy uptake of the rainwater as the most plausible mechanism
resulting in the observed diameter increases.
Foliar water uptake has been described for many species, especially in drought
stress conditions, improving photosynthetic performance and growth and is now
considered to be a widespread phenomenon (Dawson, 1998; Burgess & Dawson,
2004; e.g. Breshears et al., 2008; Limm et al., 2009; Simonin et al., 2009; Goldsmith
et al., 2012). While the pathways for foliar uptake are not entirely unravelled, the
cuticle (Yates & Hutley, 1995; Limm & Dawson, 2010), trichomes (Franke, 1967) and
hydathodes (Martin & von Willert, 2000) have been identified as gateways for water
uptake, while stomatal pores used to be expected not to allow penetration of water
films (Schönherr & Bukovac, 1972). Recently, however, Burkhardt et al. (2012)
showed that stomatal penetration of water is possible, especially in the presence of
salts. Hence, given their trichomes and salt exclusion glands, mangrove species
seem well fit to allow foliar absorption. Unlike in several other foliar water uptake
studies, no reverse sap flow was noted during rain events. It is, however, possible
that the rainwater was directly transported to the storage compartments or only
occurred in specific parts of the xylem. The latter would be in agreement with the
patchy growth pattern that has been noticed for Avicennia (Schmitz et al., 2008).
Independent of the mechanism of rainwater uptake, it is clear that the rain events
are crucial for the survival of both Rhizophora and Avicennia as without rain, both
species clearly suffered from the stress conditions caused by the saline
environment, resulting in highly negative soil water potentials (Figure 7.16). Despite
Chapter 7
160
periods of slight diameter increase, days characterised by high morning or evening
VPD caused diameters for both species to decline on average during periods without
rain, indicating that at this location, both species are functioning close to their
hydraulic limits. In these circumstances, only rain seems to allow for sufficient
hydraulic recovery.
Endogenous regulation versus environmental dynamics
From the above, it seems that stem diameter variations and coupled growth are the
result of both endogenous control and environmental dynamics. This has previously
been suggested for growth patterns of leaves and roots (Walter & Schurr, 2005). This
implies that, to allow correct predictions of plant behaviour based on mechanistic
modelling, the latter must also include these endogenous adaptations, especially as
our results show that very small differences in osmotic active compound regulation
can have drastic influences on important plant physiological variables such as the
stem diameter. Next to these endogenous influences, also alternative hydraulic
pathways such as canopy water uptake will need to be included in cohesion-tension
based models.
To this end, further research is needed to unravel the complex interactions between
environmental and endogenous control of growth, whether on molecular or entire
plant level. This will include the determination of storage osmotic water potentials
and identification of osmotic active compounds, assessing the variability in xylem
and storage hydraulic resistances and further elucidating alternative hydraulic
pathways. A more thorough knowledge on how these features influence stem
diameter variations will result in more insight into why species differ in growth
patterns and, hence, which growth strategies are more beneficial, depending on
environmental conditions. Moreover, it will allow assessing the relative importance
of endogenous regulation and environmental dynamics to long-term growth.
7.5 Conclusions
Although the time lag between transpiration and root water uptake has proven to
greatly influence stem diameter variations, endogenous regulation of growth
patterns must not be neglected. We demonstrated that, despite their occurrence in
the same environment, Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa
Griff. showed markedly different stem diameter variation patterns. Based on a
Application of the Sapflow+ method in mangrove research
161
mechanistic stem diameter and flow model, these differences were attributed to
small shifts in osmotic compound loading in the stem storage compartments. In
spite of these daily differences, both species showed an average decline in stem
diameter with characteristic short-term declines when VPD was high, pointing to
drought stress. Similarly, stem diameter of both species immediately increased
during rain events. Hence, while daily differences were based on endogenous
regulation, the average growth was mainly determined by environmental dynamics.
163
8 8 General conclusions and
perspectives
The main focus of this PhD study was to improve and critically comment on
measurements of sap flux density, based on sound thermodynamic principles. In
this concluding chapter, the main findings of this research are briefly summarized.
Afterwards, the remaining unanswered questions are discussed and suggestions for
future research are put forward.
8.1 Research outcome and scientific contributions
Existing continuous sap flux density methods should be considered empirical and
necessitate calibration
Measurements of sap flow are indispensable in plant physiological research and
applications as they link hydraulic processes throughout the entire Soil Plant
Chapter 8
164
Atmosphere Continuum (Chapter 1). These measurements can be focussed on total
sap flow through the stem or a stem section or on changes in sap flux density,
allowing to assess spatial differences in sap flow (Chapter 2). Within the latter, a
distinction can be made between methods applying continuous heating and those
based on the application of heat pulses. As mentioned in Chapter 2, the continuous
Thermal Dissipation method is not derived from the basic heat conduction-
convection equation, unlike the heat pulse methods. For these heat pulse methods,
actual conditions do not differ too much from the assumptions of an ideal heater in
an infinite medium as heat pulses are rapidly dissipated in the medium. For
continuous methods, however, this is not the case, as in real life applications, finite
boundaries will limit the continuous heat dissipation. This makes theoretical
derivations from the heat conduction-convection equation as basis for continuous
heat methods difficult. This was confirmed in Chapter 3, where it was shown that
also the continuous Heat Field Deformation method should be considered empirical,
linking an empirically derived temperature ratio to sap flux density. Given their
empirical nature, these continuous methods necessitate a species-, or even tree-
specific calibration. Even though these methods have their benefits as they allow
continuous measurements, are easily applicable because of low costs and simple
methodology (TD method) or because of their high sensitivity towards a large sap
flux density range (HFD method), they should be used with caution. Moreover, these
continuous methods are more susceptible to Natural Temperature Gradients than
the heat pulse methods and require more power, making them less suited in remote
field locations. Also, wound effects are harder to take into account as it is difficult
to assess whether deviations from reference or modelled sap flux densities are due
to the empirically determined coefficients or due to actual wounding. Because of
these reasons, heat pulse methods seem more adequate to accurately determine sap
flux density.
The anisotropy of sapwood needs to be accounted for in sap flow method
development and modelling
Although acknowledged by Marshall (1958), the anisotropy of sapwood has often
been overlooked during heat pulse sap flow method development and modelling as
the existing methods and many of the models are based on the isotropic heat
conduction-convection equation for an ideal heater in an infinite medium.
Fortunately, Chapter 4 shows that, as the Compensation Heat Pulse, Tmax and Heat
Conclusions and perspectives
165
Ratio heat pulse methods are derivations from this isotropic equation, these
methods remain applicable for anisotropic sapwood. For several model applications
and recently developed adaptations of sap flux density approaches, this is, however,
not the case. Therefore, it is advised to consequently refer to the anisotropic heat
conduction-convection equation instead of the isotropic equation and to clearly
distinguish between axial, tangential and radial sapwood properties, as was done
during the development of the Sapflow+ method in Chapter 6. This will, hopefully,
avoid further confusion and future errors in modelling and method development
and interpretation.
A distinction must be made between bound and unbound water to determine
thermal wood properties based on the method of mixtures.
In Chapter 2, it was described how the Heat Ratio method was developed as a
method enabling low and reverse flows, which is of crucial importance in studying
hydraulic redistribution processes (Chapter 1). The developers of this method
preferred not to determine axial thermal diffusivity based on the heat pulse itself as
was proposed for the Tmax method (Chapter 2) as this method necessitates zero
flows and is susceptible to errors. Unlike for the Tmax method, a deviation in
thermal diffusivity will lead to a percentually equal deviation in heat velocity for the
HR method. Therefore, thermal diffusivity determination was based on a method of
mixtures for a single cell model, taking into account volumetric heat capacity and
thermal conductivity of wood, air and water. This way, axial thermal diffusivity can
be derived based on a single wood core from which dry wood density and water
content are determined. However, in this method of mixtures, no distinction was
made between bound and unbound water, inducing an error which is dependent on
dry wood density and water content (Chapter 5). Therefore, a new equation was
proposed, taking into account the amount of bound water based on the fibre
saturation point of the sapwood. Although more accurate, this correction
necessitates a good estimate of the fibre saturation point, a parameter which can
not readily be measured and must be derived based on an empirical relation with
dry wood density.
Directly fitting measured temperature changes on axial and tangential positions
from the heater to the anisotropic heat conduction-convection equations allows
for independent estimation of heat velocity and thermal wood properties.
Chapter 8
166
In response to the limited measurement range of the Compensaion Heat Pulse,
Tmax and Heat Ratio method and the difficulties to accurately determine axial
thermal diffusivity, needed to calculate heat velocity for both the Tmax and Heat
Ratio method, an improved method, the Sapflow+ method, was proposed (Chapter
6). This method directly fits the anisotropic heat conduction-convection equation
for an ideal heater in an infinite medium to the temperature profiles measured both
axially and tangentially from the heater. The combination of these axial and
tangential measurements is necessary for the method to be sensitive towards the
entire naturally occurring sap flux density range, a feature that is not present in
previously developed heat pulse methods, even though it is applied in the
continuous Heat Field Deformation method. The Sapflow+ method has the
advantage that heat pulse velocity is determined independently from thermal wood
properties. Moreover, these properties are simultaneously estimated during the
curve fitting procedure, allowing for water content determination. This method was
validated both in laboratory conditions on cut stem segments (Chapter 6) and in
mangrove field conditions (Chapter 7). During the field experiment, the Sapflow+
method performed well in determining heat velocity and allowed the assessment of
long-term water content variation. Further validation experiments, in which a better
hardware design is coupled to independent water content estimates, should be
conducted to investigate the cause of the short-term water content variation and the
observed noise.
Small shifts in osmotic loading of the storage tissue can result in markedly
different stem diameter variation patterns.
Stem diameter variations are functionally explained by the time lag between the
transpiration at leaf level and the water uptake at root level, caused by the hydraulic
resistance between the two (Chapter 1). Because of this time lag, stem diameters
typically decline in the morning and increase again in the late afternoon. This same
time lag explains the reverse pattern for CAM plants, as these plants open their
stomata at night and close them during the day. In Chapter 7, however, we showed
that another mechanism must be involved in stem diameter changes as for
Rhizophora, the stem diameter increased in the morning and decreased in the
afternoon, even though stomata were closed during night-time. We hypothesize that
this remarkable pattern is caused by endogenous osmotic regulation of the storage
water potential which allows refilling of the storage tissues. From our modelling
Conclusions and perspectives
167
results, small shifts in osmotic loading can lead to markedly different stem
diameter variations patterns. This conclusion has significant implications for
hydraulic plant modelling as, besides environmental dynamics, this endogenous
control needs to be taken into account to accurately predict plant growth.
8.2 Future perspectives
Increasing the accuracy of sap flow measurements is crucial to assess plant water
use, investigate hydraulic pathways and validate hydrodynamic plant models. This
PhD study attempted to improve sap flow methodology by pointing to some flaws in
existing methods, proposing corrections and presenting an improved approach to
determine sap flux density and thermal sapwood properties. Nevertheless, still
many questions related to sap flow measurement methodology remain unanswered.
These questions together with suggestions for future research are listed below.
Unravelling the mechanisms of short and long term wounding
As indicated in Chapter 2 and Chapter 6, heat velocity measurements are
influenced by wound effects, comprising both short and long-term effects. When
inserting measurement and heater needles in the plant xylem, flow is locally
obstructed which has a direct influence on heat velocity measurements, both for the
continuous and the heat pulse methods, as has been shown based on Finite Element
Modelling (Swanson & Whitfield, 1981; e.g. Burgess et al., 2001a; Green et al., 2003;
Wullschleger et al., 2011). Even though the influence of flow obstruction has been
assessed in various models by implementing obstruction zones as regions of zero
flow with a width proportional to the installed needle diameter, further research
needs to be conducted to determine the actual shape and variability of the xylem
zone influenced by needle insertion. It is likely that not only width, but also length
of the obstructed zone will be dependent on needle diameter. Moreover, both width
and length will depend on thermal wood properties as well. Together with this flow
obstruction pattern, also local alteration of sapwood properties such as wood
density, fibre direction and water content due to drilling and needle installation
need to be further investigated (Barrett et al., 1995). Research on these small-scale
phenomena poses, however, several challenges. By varying the width and length of
flow obstruction zones in Finite Element Models, combined with varying wood
properties, a more profound insight on the effects of wounding on sap flux density
Chapter 8
168
measurements will be obtained. Nevertheless, more advanced methods will be
needed to assess wound effects in actual plants. In this respect, a combination of
Magnetic Resonance Imaging and wood anatomical studies seems most suited to
investigate short-term wound effects for different tree species.
Next to these short-term effects, needle installation also has consequences on the
longer term as the defence mechanisms of trees will react to the intrusion of this
foreign material. Production of resin and formation of wound tissue will alter wood
properties and, hence, heat dissipation in the sapwood in the longer term (Moore et
al., 2009). As these influences can be avoided by regularly reinstalling the sensors,
little attention has thus far been paid to long-term wounding. Nevertheless, for long
measurement periods, attention must be paid not to falsely interpret changes in sap
flux density caused by this long-term effect. It would be interesting to set-up an
experiment during which sap flux density of several species is measured, applying
both stationary sensors and sensors that are frequently relocated on the same tree.
This way, an easy assessment of the effect of long-term wounding could be
obtained. Additionally, pinning experiments may provide further inside in the
anatomical development of wound tissue.
Accounting for differences in wood anatomy in heat based sap flow methods
In Chapter 2 it was mentioned that Clearwater et al. (1999) proposed a correction
factor for the Thermal Dissipation method for those cases where part of the probe
was in contact with nonconducting xylem or bark, as heat will also be dissipated in
these tissues while they do not contribute to the sap flow. Similarly, it can be
expected that additional corrections are needed when measuring in sapwood
characterized by a non-uniform distribution of sap conducting elements and/or
other functional tissues. While such correction factors can be derived empirically for
the measured species (Swanson, 1994), a more mechanistic approach, in which
different vessel sizes and tissue characteristics are implemented in sap flow method
models, will increase our knowledge as to how these factors influence sap flux
density measurements. Similarly, it might be interesting to model and assess the
impact of radial and tangential flows as sap flux density methods only take axial
flow into account, although for most species axial and tangential flows will only
have a marginal contribution to total stem flow.
Conclusions and perspectives
169
Further optimization of water content measurements with the Sapflow+ method
The Sapflow+ method (Chapter 6) was developed to allow heat velocity
measurements across the entire naturally occurring sap flux density range,
independent of thermal sapwood properties. Moreover, as the latter were
simultaneously obtained from the curve fitting procedure, the Sapflow+ method
also enables water content determination. However, the method was only tested in
lab conditions on a single species. Further lab validation on other species is
necessary to confirm its applicability.
Even though during a field experiment the Sapflow+ method allowed heat-velocity
determination and revealed long-term water content patterns (Chapter 7), short-
term water content profiles were susceptible to noise. The cause of this scattering in
field conditions needs to be further investigated, based on validation experiments in
which an independent measure of sapwood water content can be obtained. To this
end, water contents can be determined based on wood core sampling or Magnetic
Resonance Imaging. These methods, however, are not evident. Water content
determination based on wood core sampling requires careful core drilling and
handling as water content may be influenced by evaporation or water absorption.
Magnetic Resonance Imaging, on the other hand, remains difficult to apply in field
conditions and needs highly specified parameter tuning. Nevertheless, both
methods would be interesting to compare with the Sapflow+ method. Recently,
Frequency Domain Reflectometry has been put forward as an accurate method to
determine sapwood water content. Combining this method with the Sapflow+
method may allow pinpointing the advantages and disadvantages of both methods,
both in laboratory and field conditions.
Integration of stem water content as variable in plant physiological research and
modelling
So far, stem water content has often been neglected as an important plant
physiological variable because of its impractical determination. Nevertheless, the
Sapflow+ method holds the promise of enabling stem water content measurements,
enabling the applicability of stem water content as an indicator for drought stress
or vulnerability to insect or fungus colonisation. Moreover, it can be related to water
capacitance, stem diameter variations and cavitation events. As such, stem water
content could be an interesting variable to integrate in hydrodynamic plant models.
Chapter 8
170
Unravelling the importance of endogenous control of stem diameter changes and
coupled growth
In Chapter 7 it was shown that two species influenced by the same environmental
dynamics can show entirely different patterns in stem diameter variation, pointing
to endogenous control of stem diameter changes and growth. The mechanisms
behind this endogenous regulation, however, still need to be clarified in further
studies. Given the complexity of growth regulation, studies will have to focus on the
molecular, tissue as well as the entire plant level. Within these studies, plant water
and carbon relations need to be coupled, assessing how carbohydrate metabolism
influences osmotic storage potential and is linked to diel growth dynamics. By
sampling the bark and xylem tissue, diel patterns of osmolite concentrations can be
obtained to confirm the modelling results. Based on chemical analysis, it can then
be derived which of the osmotic compounds has the greatest influence on storage
water potential and could reveal possible species specific metabolism pathways. By
varying the salinity and nutrient concentration of the soil water in combination with
varying microclimatic conditions in a controlled environment, their influence on the
daily stem diameter variations can be assessed, further elucidating the cause of the
observed shrinkage events and the difference in pattern between the two species.
Additionally, labelled isotope experiments could be applied to confirm the canopy
water uptake hypothesis and provide insights into the water uptake pathway.
171
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193
Summary
Just as carbon, water is indispensable for plants to develop and grow. A lack of
water causes turgor loss in plant cells which prevents further expansion of these
cells and the coupled incorporation of carbon sources in the cell wall. This inhibits
growth and, if this water scarcity continues, plant dimensions such as the stem
diameter will start to decrease. Finally the plant will lose its vital functions and die.
Worldwide, sap flow methods are applied to monitor plant water status and validate
vegetation models. These methods determine flow direction as well as relative and
absolute flow, forming the link between plant water uptake, release and storage.
Hence, whether to assess the correct irrigation dose, to monitor forest vitality or to
obtain trustworthy modelling results, reliable sap flow measurements are
indispensable.
The most commonly applied sap flow methods are based on heat dissipation in the
sapwood. Within this group, a distinction can be made between those methods
determining the total flow per time inside a stem or stem section and those
assessing sap flux density, the flow per surface per time. While the former are
widely applied in irrigation and other applications necessitating an estimation of
total plant water use, the latter are applied to investigate specific hydraulic
pathways and processes as they allow to distinguish spatial patterns in sap flow,
both axially, radially and azimuthally.
In this PhD study, the accuracy and applicability of the most important sap flux
density methods were investigated. To this end, the underlying thermodynamic
theory was studied, Finite Element Modelling (FEM) conducted and lab experiments
Summary
194
on cut tree stem segments were undertaken, complemented with a field study on
Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff.
By investigating the thermodynamic interpretation of the thermal diffusivity as
sapwood property, it became clear that the link between the Heat Field Deformation
(HFD) temperature ratio and sap flux density, based on this thermal diffusivity, was
incorrect. It was concluded that therefore, the continuous HFD method should be
considered merely empirical, similar to the Thermal Dissipation method. Moreover,
based on FEM, an improved empirical correlation between the HFD temperature
ratio and sap flux density was proposed.
Also for the methods based on the application of heat pulses, a flaw in the basic
theory was noted. These methods are based on the isotropic heat conduction-
convection equation for an ideal heater in an infinite medium. Sapwood, however, is
known to be anisotropic. Fortunately, the Compensation Heat Pulse, Tmax as well as
the Heat Ratio method are based on derivations of this basic equation in a way that
is independent of the assumption of isotropy. Hence, for these methods the results
are still theoretically correct. Nevertheless, attention should be paid to apply the
correct anisotropic equation in modelling and method development, as recent
examples show that by neglecting anisotropy, errors can be induced.
Within the heat pulse sap flux density methods, the Heat Ratio method enables
measurements of low and reverse flow, unlike the Compensation Heat Pulse and
Tmax method. This method, however, is dependent on accurate estimations of axial
thermal sapwood diffusivity. In this PhD, it was shown that in the currently applied
method of mixtures to determine this diffusivity, no distinction was made between
bound and unbound water, resulting in over- or underestimations of axial thermal
diffusivity dependent on the dry sapwood density and sapwood water content. A
correction to this method was proposed, differentiating between bound and
unbound water based on the fibre saturation point. This correction has the
disadvantage that fibre saturation point is a sapwood characteristic that is not
measurable in-situ and, hence, has to be estimated based on dry sapwood density.
In response to the difficulties encountered when studying the different sap flux
density methods, a new method was developed: the Sapflow+ method. This method
is based on a curve fitting procedure during which the anisotropic heat conduction-
convection equation is directly fitted to measured temperature profiles located both
Summary
195
axially and tangentially from the heater. As was shown by the conducted
identifiability analysis and the lab experiments on stem segments of Fagus sylvatica
L., the Sapflow+ method enables simultaneous measurements of heat velocity,
across the entire naturally occurring range, and thermal sapwood properties, from
which sap flux density and sapwood water content can be derived. The applicability
of the method to determine heat velocity was confirmed in a field experiment on
Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff. For the
determination of sapwood water content, further validation experiments and
possible optimization of the method are needed.
Next to providing an opportunity to test the Sapflow+ method in harsh field
conditions, the experiments conducted on Avicennia and Rhizophora led to the
remarkable finding that both species show a completely different pattern in stem
diameter variation, despite being influenced by the same environmental conditions.
This led to the hypothesis that endogenous control of stem diameter fluctuations
and growth might be much more crucial than previously assumed and could play an
important role in plant growth strategies.
In conclusion, the presented PhD study has exposed some limitations of and
inaccuracies in existing sap flux density methods and has provided an alternative
based on correct theoretical principles. This Sapflow+ method is sensitive towards
the entire naturally occurring sap flow range and holds the promise of accurately
determining sapwood water content.
.
197
Samenvatting
Net zoals koolstof is water onontbeerlijk voor de ontwikkeling en groei van planten.
Een gebrek aan water zorg voor turgorverlies in de plantcellen. Dit verhindert
expansie van deze cellen en de gekoppelde inbouw van koolstofbronnen in de
celwand waardoor verdere groei onmogelijk wordt. Als deze waterschaarste
aanhoudt, nemen plantdimensies zoals stam diameter af en verliest de plant finaal
zijn vitale functies waardoor ze afsterft.
Wereldwijd worden sapstroommethoden gebruikt om de plantwaterstatus op te
volgen en vegetatiemodellen te valideren. Deze methoden bepalen zowel de
stroomrichting als de relatieve en absolute hoeveelheid sapstroom, waardoor het
verband kan gelegd worden tussen de wateropname, -vrijstelling en -opslag van de
plant. Bij deze meetmethoden is accuraatheid van de sapstroombepaling
onontbeerlijk, of het nu gaat om de bepaling van de correctie irrigatiedosis, het
opvolgen van bosvitaliteit of om betrouwbare modelresultaten te bekomen.
De meest gebruikte sapstroommethoden zijn gebaseerd op de verspreiding van
warmte in het spinthout. Binnen deze groep kan verder onderscheid gemaakt
worden tussen de methoden die de totale hoeveelheid sapstroom per tijd in een
stam of stamsectie bepalen en deze die de sapstroomdichtheid bepalen, de
hoeveelheid sapstroom doorheen een gegeven oppervlakte per tijd. Waar de
eerstgenoemde vooral ingezet worden voor irrigatietoepassingen en andere
applicaties waarbij een inschatting van het totale waterverbruik van de plant beoogd
wordt, worden de laatstgenoemde vooral aangewend om specifieke hydraulische
routes en processen in de plant te onderzoeken, aangezien deze methodes toelaten
om ruimtelijke verschillen, zowel axiaal, radiaal als azimuthaal, in de
sapstroomdichtheid te bepalen.
Samenvatting
198
In dit doctoraatonderzoek werden de accuraatheid en toepasbaarheid van de
belangrijkste sapstroomdichtheidmethoden onderzocht. Hiertoe werd de
onderliggende thermodynamische theorie bestudeerd, werden Finite Element
Modellen (FEM) toegepast en werden labo experimenten uitgevoerd op afgezaagde
stamsegmenten, aangevuld met een veldstudie waarbij op Avicennia marina
(Forssk.) Vierh. en Rhizophora stylosa Griff. werd gemeten.
Door de thermodynamische betekenis van de thermische diffusiviteit als
spinthouteigenschap onder de loep te nemen, werd duidelijk dat de op deze
parameter gebaseerde link tussen the Heat Field Deformation (HFD)
temperatuurratio en sapstroomdichtheid, incorrect was. Op basis daarvan werd
besloten dat de continue HFD methode, net zoals de Thermal Dissipation methode,
als empirisch moet beschouwd worden. Bovendien werd op basis van FEM een
verbeterde empirische correlatie tussen de HFD temperatuurratio en
sapstroomdichtheid voorgesteld.
Ook voor de methoden gebaseerd op de applicatie van een warmtepuls werd een
gebrek in de toegepaste theorie bemerkt. Deze methoden zijn namelijk gebaseerd
op de isotrope warmteconductie-convectievergelijking, ontwikkeld voor een ideale
verwarmingsnaald in een oneindig groot medium. Het is echter bekend dat
spinthout anisotrope karakteristieken heeft. Gelukkig zijn zowel de Compensation
Heat Pulse, Tmax als Heat Ratio methode gebaseerd op afleidingen van deze
isotrope vergelijking waarbij de resultaten onafhankelijk zijn van de assumptie van
isotropie en geldig blijven voor anisotrope media. De metingen bekomen via deze
methoden zijn theoretisch dus nog steeds correct. Toch moet er op gelet worden dat
de correcte anisotrope vergelijkingen worden toegepast in modelleerstudies en bij
het ontwikkelen van nieuwe warmte gebaseerde methoden aangezien recente
voorbeelden aantonen dat het verwaarlozen van het anisotroop karakter van
spinthout tot fouten kan leiden.
Binnen de bestaande warmtepulsmethoden, laat de Heat Ratio methode, in
tegenstelling tot de Compensation Heat Pulse en Tmax methode, toe om lage en
omgekeerde sapstroom te meten. Deze methode is echter afhankelijk van een
nauwkeurige bepaling van de axiale thermische diffusiviteit. In dit
doctoraatonderzoek werd aangetoond dat in de huidig toegepaste
combinatiemethode geen onderscheid wordt gemaakt tussen gebonden en
Samenvatting
199
ongebonden water. Dit kan tot over- of onderschattingen van de axiale thermische
diffusiviteit leiden, afhankelijk van de droge dichtheid en het vochtgehalte van het
spinthout. Een correctie werd voorgesteld waarbij het onderscheid tussen gebonden
en ongebonden water gemaakt wordt op basis van het vezelverzadigingspunt van
het spinthout. Deze correctie heeft als nadeel dat het vezelverzadigingspunt een
spinthouteigenschap is die moeilijk in situ kan bepaald worden, en dus geschat
moet worden op basis van de droge densiteit van het spinthout.
Als antwoord op de beperkingen waarop gebotst werd tijdens het bestuderen van de
bestaande sapstroomdichtheidmethoden, werd een nieuwe methode ontwikkeld: de
Sapflow+ methode. Deze methode is gebaseerd op een curve fitting procedure
waarbij de anisotrope warmteconductie-convectievergelijking rechtstreeks gefit
wordt aan opgemeten temperatuurprofielen op specifieke afstanden axiaal en
tangentieel van de warmtenaald. Zoals aangetoond via een
identificeerbaarheidsanalyse en labo experimenten op stamsegmenten van Fagus
sylvatica L., laat de Sapflow+ methode toe om gelijktijdig warmtesnelheden, over het
volledig natuurlijk voorkomende bereik, en thermische eigenschappen van het
spinthout op te meten. Hieruit kan dan sapstroomdichtheid en
spinthoutvochtgehalte bepaald worden. De toepasbaarheid van de Sapflow+
methode voor het bepalen van warmtesnelheden werd bevestigd tijdens een
veldexperiment via metingen op Avicennia marina (Forssk.) Vierh. en Rhizophora
stylosa Griff. Voor de bepaling van het spinthoutvochtgehalte zijn additionele
validatie-experimenten en mogelijks verdere optimalisatie van de methode nodig
Naast de mogelijkheid om de Sapflow+ methode te testen in moeilijke
veldomstandigheden, hebben de uitgevoerde experimenten op Avicennia en
Rhizophora tot de merkwaardige vaststelling geleid dat beide soorten een volledig
verschillend stamdiametervariatiepatroon vertonen, ondanks dat ze door dezelfde
omgevingsomstandigheden beïnvloed worden. Dit leidde tot de hypothese dat
endogene controle van de stamdiameterfluctuaties en groei belangrijker kan zijn
dan aanvankelijk werd gedacht en bovendien een beduidende rol kan spelen in
plantgroeistrategieën.
Samenvattend heeft dit doctoraatonderzoek een aantal beperkingen en
onnauwkeurigheden van bestaande sapstroomdichtheidmethoden blootgelegd en
biedt het een alternatief aan, gebaseerd op correcte thermodynamische principes.
Samenvatting
200
Dit alternatief, de Sapflow+ methode, is gevoelig tegenover het volledig natuurlijk
voorkomend sapstroombereik en houdt de belofte in accurate vochtgehaltes van
spinthout te kunnen bepalen.
.
201
Curriculum vitae
Personal information Name: Maurits Willem Vandegehuchte
Date of birth: 20 February 1987
Place of birth: Oostende (Belgium)
Nationality: Belgian
Address: Lisbloemstraat 45, 9000 Gent
Tel: +32 473 32 22 54
E-mail: [email protected]
Education
2007-2009 M.Sc. in Bioscience Engineering (Environmental Technology),
Faculty of Bioscience Engineering, Ghent University, Ghent
(Summa Cum Laude)
Master thesis:
Performed at the Laboratory of Plant Ecology, Ghent
University, Gent in collaboration with the ‘Institut d’Olivier’,
Sousse, Tunisia.
Title: “Evaluation of several irrigation techniques and sap
flow variation for olive tree Olea europaea L. ‘Meski’”.
Promoter: prof. dr. ir. Kathy Steppe
Curriculum vitae
202
2004-2007 B.Sc. in Bioscience Engineering, Faculty of Bioscience Engineering,
Ghent University, Ghent (Magna Cum Laude)
1998-2004 Secondary school, Science-Mathematics, Onze-Lieve-
Vrouwecollege, Oostende
Additional education
2009-2013 Doctoral training programme in Bioscience Engineering,
Faculty of Bioscience Engineering, Ghent University
Courses followed in the framework of this programme:
Wood technology: material characteristics (2009-2010)
Multivariate data analysis (2009-2010)
Advanced academic English: writing skills (2010-2011)
Effective Scientific Communication (2010-2011)
Quality Research Skills (2010-2011)
Personal Effectiveness (2010-2011)
Leading, Following and Collaborating (2010-2011)
Applied isotope studies (2011-2012)
Career management: applying for a postdoctoral job (2013)
April 2012 Certificate of succeeding a four day Tree Climbing PRO
course organized by The Tree Climbing Company
November 2009 Certificate of instructor at youth work recognized by the
Agency of Social-Cultural Work of the Flemish Government
September 2009 Certificate of succeeding the course on international
cooperation and development issues (North-South relations)
organized by the Belgian Technical Cooperaton (BTC)
Professional experience
2009-2013 Research fellow of the Research Foundation – Flanders
(FWO, Flanders, Belgium). The research as preparation for
this doctoral thesis was conducted at the Department of
Curriculum vitae
203
Applied Ecology and Environmental Biology (Laboratory of
Plant Ecology) of the Ghent University, Gent.
Other scientific activities
June 2013 Member of the scientific committee of the 9th International
Workshop on Sap Flow, Ghent, Belgium, 4-7 June 2013
July-October 2012 Research stay at Moreton Bay Research Station, Queensland
University, North Stradbroke Island, Australia in
collaboration with the Groundwater Research Centre, Civil
Engineering, Queensland University, Bribane, Australia.
Mangrove water relations research in the framework of the
PhD.
April-May 2012 Research stay at Wageningen NMR Centre, Wageningen
University, the Netherlands to be instructed in NMR wood
water content research.
October 2010 Research stay at the Institute of Forest Ecology, Mendel
University of Agriculture and Forestry, Brno, Czech Republic
to discuss sap flow measurement methods with prof.
Nadezhdina and prof. Cermak.
2009-2013 Review tasks for Tree Physiology, Plant and Soil,
International Journal of Thermal Sciences, Trees - Structure
and Function, Hydrological Processes and Australian Journal
of Multi-disciplinary Engineering.
Grants and prizes
July 2012 Grant from the Research Foundation – Flanders (FWO –
Vlaanderen) for the research visit at the University of
Queensland, Australia.
October 2010 Scholarships from the Department of Education and
Training (Flemish Government) and the Czech Republic
Ministry of Education, Youth and Sport for the research visit
at the Mendel University, Brno, Czech Republic.
Curriculum vitae
204
October 2009 PhD fellowship from the Research Foundation – Flanders
(FWO – Vlaanderen) for the PhD research at Ghent
University, Belgium
September 2009 Bayer Plant Science award from Bayer Plant and Bayer Crop
Science for the master thesis ‘Evaluation of several irrigation
techniques and sap flow variation for olive tree Olea
europaea L. ‘Meski’’.
Educational activities
2009-2013 Guidance of practical courses and technical lectures for
the courses “Ecophysiology”, “Plant-Water Relations” and
“Ecology”.
2012-2013 Tutor of the M.Sc. thesis of Mieke Van Houtte (Electrical
Resistivity Tomography (ERT) to establish wood water
content patterns in living trees), Stefanie de Groote
(Canopy water uptake in the mangrove species Avicennia
marina), Michiel Hubeau (Water transport and growth
patterns in mangrove species Rhizophora) and Niels De
Baerdemaker (Assessing the water use strategies of
Banksia aemula).
2011-2012 Tutor of the M.Sc. thesis of Caroline Van der Heyden
(Seizoenale relatieve verandering in sapstroomdichtheid
en vochtgehalte van het spinthout van beuk (Fagus
sylvatica L.)) and Dries Vermassen (Validatie van de
Sapflow+ sensor: hoe nauwkeurig wordt
sapstroomdichtheid en vochtgehalte van het spinthout
door deze methode bepaald?)
2010-2011 Tutor of the M.Sc. thesis of Lidewei Vergeynst (Changes
in temperature and stem water content evoke erroneous
sap flux density estimates with. Thermal Dissipation
Probes) and Bart Van de Wal (Ecophysiology of mangrove
in Australia: hydraulic functioning).
Curriculum vitae
205
Publications
International publications with peer review
Vandegehuchte, M. W., Braham, M., Lemeur, R. & Steppe, K. (2012). The importance
of sap flow measurements to estimate actual water use of Meski olive trees under
different irrigation regimes in Tunisia. Irrigation and Drainage, 61: 645-656..
Vandegehuchte, M.W. & Steppe, K. (2012) Comment on “Sap flow measurements by a
single thermal dissipation probe: exploring the transient regime” — Ann. For. Sci. 66
(2009) by Mahjoub et al. and “Sap flow measurement by a single thermal dissipation
probe in transient regime: implementation of the method and test under field
conditions” — Ann. For. Sci. 1-9 (2012) by Masmoudi et al. Annals of Forest Science,
69: 769-771.
Vandegehuchte, M.W. & Steppe, K. (2012). Use of the correct heat conduction-
convection equation as basis for heat pulse sap flow methods in anisotropic wood.
Journal of Experimental Botany, 63: 2833-2839.
Vandegehuchte, M.W. & Steppe, K. (2012). Interpreting the Heat Field Deformation
method: Erroneous use of thermal diffusivity and improved correlation between
temperature ratio and sap flux density. Agricultural and Forest Meteorology, 162-
163: 91-97.
Vandegehuchte, M.W. & Steppe, K. (2012). Improving sap flux density measurements
by correctly determining thermal diffusivity, differentiating between bound and
unbound water. Tree Physiology, 32: 930-942.
Vandegehuchte, M. W. & Steppe, K. (2012). A triple-probe heat pulse method for
measurement of thermal diffusivity in trees. Agricultural and Forest Meteorology.
160: 90-99.
Curriculum vitae
206
Vandegehuchte, M.W. & Steppe, K. (2012). Sapflow+: a four-needle heat pulse sap
flow sensor enabling nonempirical sap flux density and water content
measurements. New Phytologist, 196: 306-317.
Vandegehuchte, M.W. & Steppe, K. (2012). Sap flux density measurement methods:
working principles and applicability. Functional Plant Biology (accepted).
Reyes-Acosta, J. L., Vandegehuchte, M. W., Steppe, K. & Lubczynski, M. W( 2012).
Novel, cyclic thermal dissipation (CHD) method for the correction of natural
temperature gradients in sap flow measurements. Part 2. Laboratory validation. Tree
Physiology, 32: 930-42
Nadezhdina, N., Vandegehuchte, M.W. & Steppe, K. (2012). Sap flux density
measurements based on the heat field deformation method. Trees - Structure and
Function, 26: 1439-1448.
Proceedings
Vandegehuchte, M.W. & Steppe, K. (2012). Finite Element Analysis as Aid in
Understanding Heat Based Sap Flow Methods with Linear Heating. 8th International
Symposium on Sap Flow, 951: 63-70.
Oral presentations
Vandegehuchte, M.W., Nadezhdina, N. & Steppe, K. (2011) Improved thermodynamic
approach for Heat Field Deformation sap flow measurements. 8th International Sap
Flow Workshop, Volterra, Italy, 8-12 May 2011.
Reyes-Acosta, L.J., Vandegehuchte, M.W., Steppe, K. & Lubcsynski, M.W. (2011)
Natural thermal gradient (NTG) bias on sap flow measurements when using Thermal
Dissipation Probes and Heat Field Deformation sensors: errors and corrections by
Curriculum vitae
207
applying an alternated power methodology.8th International Sap Flow Workshop,
Volterra, Italy, 8-12 May 2011
Steppe K., Vandegehuchte M.W., Van de Wal B.A.E., Hoste P., Guyot A., Lovelock C.E.,
Lockington D. (2013) Reverse sap flow in mangroves: do these trees drink rainwater
through their canopy? International Symposium on Wood Structure in Plant Biology
and Ecology (WSE), Naples, Italy, 17-20 April 2013.
Vandegehuchte, M.W., Guyot, A., Lockington, D.A. & Steppe, K. (2013) Stem diameter
variation: endogenous regulation versus environmental dynamics and its implication
for functional modelling. 7th International Conference on Functional-Structural Plant
Models, Saariselkä, Finland, 9-14 June 2013 (accepted)
Vandegehuchte, M.W. & Steppe, K. (2013) Eliminating the heat input as parameter in
the Sapflow+ method. 9th International Sap Flow Workshop, Ghent, Belgium, 4-7
June 2013 (accepted)
de Sousa, E.F., Santolin, M.A., Vandegehuchte, M.W., Compostrini, E. & de Jesus
Soares, K. (2013). Development of a mathematical model and its numerical solution
to estimate sap flow applying a transient heating system. 9th International Sap Flow
Workshop, Ghent, Belgium, 4-7 June 2013 (accepted)
Poster presentations
Vergeynst, L.L., Vandegehuchte, M.W., McGuire, M.A., Teskey, R.O. & Steppe, K.
(2011) Changes in temperature and stem water content evoke erroneous sap flux
density estimates with Thermal Dissipation Probes. 8th International Sap Flow
Workshop, Volterra, Italy, 8-12 May 2011
Guyot, A., White, A., Vandegehuchte, M.W., Steppe, K. & Lockington, D.A. (2013)
Atmosphere-Vegetation-Groundwater interactions: a case study in the context of the
subtropical coastal sandy mass aquifers from Eastern Australia. Geophysical
Research Abstracts, 15, EGU, Vienna, Austria, 7-12 April 2013
Vandegehuchte, M.W., Burgess, S.S.O., Downey, A & Steppe, K. (2013) Stem
temperature influence on heat pulse sap flux density measurements. 9th
International Sap Flow Workshop, Ghent, Belgium, 4-7 June 2013 (accepted)
Lubczynski, M.W., Reyes-Acosta, L.J., Chavarro-Rincon, D., Vandegehuchte, M.W.,
Roy, J., & Steppe, K. (2013) Cyclic heat dissipation (CHD) method for the correction
Curriculum vitae
208
of natural temperature gradients in sap flow measurements. 9th International Sap
Flow Workshop, Ghent, Belgium, 4-7 June 2013 (accepted)